Discovery Logo
Sign In
Search
Paper
Search Paper
R Discovery for Libraries Pricing Sign In
  • Home iconHome
  • My Feed iconMy Feed
  • Search Papers iconSearch Papers
  • Library iconLibrary
  • Explore iconExplore
  • Ask R Discovery iconAsk R Discovery Star Left icon
  • Literature Review iconLiterature Review NEW
  • Chat PDF iconChat PDF Star Left icon
  • Citation Generator iconCitation Generator
  • Chrome Extension iconChrome Extension
    External link
  • Use on ChatGPT iconUse on ChatGPT
    External link
  • iOS App iconiOS App
    External link
  • Android App iconAndroid App
    External link
  • Contact Us iconContact Us
    External link
  • Paperpal iconPaperpal
    External link
  • Mind the Graph iconMind the Graph
    External link
  • Journal Finder iconJournal Finder
    External link
Discovery Logo menuClose menu
  • Home iconHome
  • My Feed iconMy Feed
  • Search Papers iconSearch Papers
  • Library iconLibrary
  • Explore iconExplore
  • Ask R Discovery iconAsk R Discovery Star Left icon
  • Literature Review iconLiterature Review NEW
  • Chat PDF iconChat PDF Star Left icon
  • Citation Generator iconCitation Generator
  • Chrome Extension iconChrome Extension
    External link
  • Use on ChatGPT iconUse on ChatGPT
    External link
  • iOS App iconiOS App
    External link
  • Android App iconAndroid App
    External link
  • Contact Us iconContact Us
    External link
  • Paperpal iconPaperpal
    External link
  • Mind the Graph iconMind the Graph
    External link
  • Journal Finder iconJournal Finder
    External link
features
  • Audio Papers iconAudio Papers
  • Paper Translation iconPaper Translation
  • Chrome Extension iconChrome Extension
Content Type
  • Journal Articles iconJournal Articles
  • Conference Papers iconConference Papers
  • Preprints iconPreprints
  • Seminars by Cassyni iconSeminars by Cassyni
More
  • R Discovery for Libraries iconR Discovery for Libraries
  • Research Areas iconResearch Areas
  • Topics iconTopics
  • Resources iconResources

Related Topics

  • Probability Distribution Function
  • Probability Distribution Function
  • Probability Density
  • Probability Density

Articles published on Probability Functions

Authors
Select Authors
Journals
Select Journals
Duration
Select Duration
8379 Search results
Sort by
Recency
  • New
  • Research Article
  • 10.1063/5.0336322
Investigation of plasma characteristics in a developed large-diameter, low-aspect ratio, radio frequency plasma source with a flat spiral antenna.
  • Jul 1, 2026
  • The Review of scientific instruments
  • Takeru Furukawa + 3 more

A large-diameter, radio frequency (RF) plasma source with an inner diameter of 53.8cm has been developed to evaluate high densification and the feasibility of such sources. This plasma source has a low aspect ratio with the source length shorter than the diameter. To evaluate the feasibility and plasma characteristics of this low-aspect-ratio device, preliminary measurements of plasma parameters, the electron energy probability function, and optical emission spectra were performed. The dependences on the RF input power and external magnetic field conditions suggest that inductively coupled plasma can be generated in the source. The results also indicate that suitable operational conditions for high-density plasma generation exist, which are related to the helicon wave dispersion relation under the available magnetic field strength.

  • New
  • Research Article
  • 10.1016/j.ress.2026.112295
A synergistic approach: multi-purpose K-nearest neighbor and active learning Kriging for efficient failure probability function estimation
  • Jul 1, 2026
  • Reliability Engineering & System Safety
  • Huanhuan Hu + 5 more

A synergistic approach: multi-purpose K-nearest neighbor and active learning Kriging for efficient failure probability function estimation

  • New
  • Research Article
  • 10.1016/j.jenvman.2026.130295
Modeling connectivity and sediment reduction with PROSEB: a study of prairie strips in agricultural catchments.
  • Jun 23, 2026
  • Journal of environmental management
  • José A Muñoz-Sánchez + 3 more

Modeling connectivity and sediment reduction with PROSEB: a study of prairie strips in agricultural catchments.

  • Research Article
  • 10.1038/s43856-026-01702-7
Deep learning approach for probabilistic pulmonary function estimation from chest X-ray and peak expiratory flow rate
  • Jun 9, 2026
  • Communications Medicine
  • Christoph Killing + 13 more

BackgroundSpirometry remains the gold standard for assessing pulmonary function. Deep learning models have demonstrated potential for estimating measurements from chest X-rays (CXR). We aim to effectively address anatomical variability and integrate probabilistic reasoning to enhance estimation reliability near diagnostic thresholds.MethodsWe developed a probabilistic machine learning framework to estimate the forced expiratory volume in the first second (FEV1) and the forced vital capacity (FVC) as measured through spirometry. Estimations use morphologically regularized CXRs and anthropometric-normalized peak expiratory flow rate (PEFR) as proxy for volumetric information unavailable in imaging. By estimating FEV1 and FVC z-scores, we decouple appearance from anatomic variability. We demonstrate our method on a multi-national cohort of pulmonary tuberculosis patients exhibiting diverse structural abnormalities and ventilatory impairments.ResultsUsing ensembles of neural networks, we analyze 982 CXR and spirometry pairs from 568 individuals. The best model achieves an area under curve (AUC) of 0.879 (FEV1; 99%CI 0.876, 0.881) and 0.853 (FVC; 99%CI 0.850, 0.856) in identifying moderate or severe lung-function impairment on a previously unseen test-set, signifying an AUC improvement of 0.144 (FEV1) and 0.118 (FVC) over previous methods. When allowing up to 10% of samples to remain unclassified due to uncertainty, AUC further rises to 0.894 (0.891, 0.896) and 0.857 (0.854, 0.860), respectively. Our method performs robustly across diverse impairment types and CXR pathologies.ConclusionsOur study shows that decoupling anatomical variability from functional assessment improves lung function estimation. Incorporation of probabilistic modeling improved diagnostic reliability around a decision threshold. Therefore, our system offers a promising approach to practical lung function estimation in settings where spirometry is unavailable.

  • Research Article
  • 10.1080/01691864.2026.2680954
Adaptive threshold-based task allocation for swarm search-and-rescue robotics in unknown environments with limited communication
  • Jun 9, 2026
  • Advanced Robotics
  • Weitao Zhao + 4 more

Task allocation is a central challenge in swarm robotics, yet most existing approaches assume known target locations or global communication, limiting their applicability in real-world search-and-rescue (SAR). This paper proposes a distributed method, the adaptive dynamic response threshold model (A-DRTM), to address SAR tasks in unknown and noisy environments under communication constraints. A-DRTM defines a task selection probability function that dynamically adjusts thresholds according to task demand disparities. Stimulation and jitter mechanisms are further incorporated to enhance flexibility and avoid local optima, improving responsiveness to environmental changes and coordination efficiency. Comprehensive simulations across varying initial positions, map sizes, robot-to-task ratios, communication ranges, and moving targets show that A-DRTM consistently outperforms six representative threshold-based algorithms. It achieves higher task completion, better resource utilisation, and stronger scalability, particularly in large-scale and communication-limited conditions.

  • Research Article
  • 10.1088/1361-6633/ae72c3
Percolation with coupled lasers: effect of non-linearities on the phase transition
  • Jun 1, 2026
  • Reports on Progress in Physics
  • Simon Mahler + 4 more

Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a platform of coupled lasers, where connectivity, interaction strength, and system size can be controlled. Using a square array of100lasers with astronomical number of possible cluster configurations, we show that the emergence of a percolating cluster corresponds to the onset of phase locking among the lasers. We also show that the percolation probability undergoes a second-order alike transition as a function of the site-occupation probability, with a threshold consistent with classical theoretical predictions. Surprisingly, we find that at low pump level, amplified mode competition (nonlinear regime) alters the effective behavior of the lasing sites and modify the nature of the percolation transition. The experimental results are interpreted by the means of a theoretical toy model with connectivity rules to the classical percolation.

  • Research Article
  • 10.1016/j.rineng.2026.110153
Multi-objective salp swarm optimization for the sizing of a hybrid renewable energy system
  • Jun 1, 2026
  • Results in Engineering
  • Intissar Khoja + 3 more

Multi-objective salp swarm optimization for the sizing of a hybrid renewable energy system

  • Research Article
  • 10.1016/j.aap.2026.108472
Analysis of duration between crashes among repeatedly crash-involved drivers using alternate unobserved-heterogeneity modeling approaches.
  • Jun 1, 2026
  • Accident; analysis and prevention
  • Dongdong Song + 6 more

Analysis of duration between crashes among repeatedly crash-involved drivers using alternate unobserved-heterogeneity modeling approaches.

  • Research Article
  • 10.1111/psyp.70333
Alpha and Theta Oscillations Differentiate Escalating Risk Levels During Reward Anticipation in Sequential Decision Making.
  • Jun 1, 2026
  • Psychophysiology
  • Eszter Tóth-Fáber + 1 more

Alpha and Theta Oscillations Differentiate Escalating Risk Levels During Reward Anticipation in Sequential Decision Making.

  • Research Article
  • 10.1002/asia.70821
Quercetin Affects Carcinogenic Phenotype of Breast and Lung Cancer Cells Differentially Through Sterol Regulation Mediated by MALAT1 Perturbation.
  • Jun 1, 2026
  • Chemistry, an Asian journal
  • Isha Rakheja + 3 more

Targeting MALAT1 in cancer treatment is an attractive strategy due to the undebatable role of this lncRNA in the disease. Small molecules toward this noncoding RNA have, in fact, entered preclinical trials, without resulting in a robust demonstration in favor of their use in therapy. To test the robustness of this method, we asked how aspects of carcinogenesis get affected when knocking down MALAT1 in different cell lines. Using two such cell lines in this study to compare side-by-side, we observed that small molecule quercetin (and its subsequent reduction of MALAT1 lncRNA levels) showed heterogenic effects on carcinogenesis, which is similarly indicated by previous literature. Further, using a combination of cell biology (including the use of 3D tumor spheroids) and bioinformatics, this study is able to pinpoint the probable function of the SREBP1 protein (which showed a significant reduction of around 50%) in affecting carcinogenesis via MALAT1, corroborating earlier reports that link MALAT1 to the sterol regulation axis. This study, in summary, notes that using MALAT1 reduction (using quercetin or otherwise) needs to be very specific in the targeting of cancer cells in order to avoid paradoxical results.

  • Research Article
  • 10.21037/jtd-2026-1-0382
Comparison of pulmonary ventilation/perfusion tomography and conventional diagnostic techniques in the diagnosis of pulmonary thromboembolism
  • May 27, 2026
  • Journal of Thoracic Disease
  • Xue Lv + 2 more

BackgroundPulmonary thromboembolism (PTE) is a common and potentially fatal cardiopulmonary vascular disease. Early and accurate diagnosis is crucial for improving patient prognosis. Computed tomography pulmonary angiography (CTPA) is widely used as a first-line imaging modality, while the clinical value of pulmonary ventilation/perfusion single-photon emission computed tomography (V/Q SPECT) in specific patient populations is increasingly recognized. However, systematic evidence comparing the diagnostic performance and corresponding patient clinical phenotypes across different imaging techniques remains limited. This study aimed to compare the application differences between V/Q SPECT and CTPA in diagnosing PTE, along with their associated clinical characteristics, physiological functional status, and risk stratification features, thereby providing evidence-based support for optimizing imaging diagnostic pathways.MethodsA retrospective case-control study was conducted, enrolling hospitalized patients diagnosed with PTE between January 1, 2017, and April 30, 2022, at a tertiary hospital in Shandong Province. Initially, 1,124 cases were retrieved via electronic medical record (EMR) and imaging databases. After screening, 726 patients were finally included: 312 in the V/Q SPECT group and 414 in the CTPA group. Demographic characteristics, clinical manifestations, laboratory indicators [D-dimer, troponin I, N-terminal pro-brain natriuretic peptide (NT-proBNP), partial pressure of arterial oxygen to the fraction of inspired oxygen (PaO2/FiO2), etc.], lower limb venous ultrasound, and echocardiographic parameters were systematically collected. Propensity score weighting was employed to balance baseline differences. Multivariable logistic regression and receiver operating characteristic (ROC) curve analyses were performed.ResultsAfter weighting, baseline characteristics were well-balanced between the two groups. Patients in the V/Q SPECT group more frequently presented with central or lobar emboli, accompanied by more significant hypoxemia and right ventricular dysfunction (RVD). Their levels of D-dimer, NT-proBNP, and myocardial injury markers were higher than those in the CTPA group. The CTPA group in our cohort predominantly consisted of patients with relatively milder clinical symptoms and biomarker profiles. Multivariable analysis revealed that elevated NT-proBNP, RVD, and lower limb deep vein thrombosis (DVT) were significantly associated with the use of V/Q SPECT. The multi-parameter combined model demonstrated good discriminative ability, with an area under the curve (AUC) of 0.832 [95% confidence interval (CI): 0.801–0.862].ConclusionsV/Q SPECT and CTPA are associated with distinct clinical phenotypes in real-world practice, largely reflecting systematic selection patterns driven by patient-specific contraindications and baseline risk profiles. In our cohort, V/Q SPECT was more commonly utilized in patients with higher clinical risk and biomarker levels, reflecting a clinical selection pattern where this modality was assigned to a more physiologically compromised population, while CTPA was applied to a relatively lower-risk cohort. The selection of imaging modality should integrate comprehensive assessment of clinical probability, biomarkers, and cardiopulmonary function to achieve individualized diagnostic decision-making.

  • Research Article
  • 10.1039/d5em00933b
Seasonal variability and source diagnostics of ambient PAHs in Agra, India, using the CBPF and their health risk evaluation.
  • May 27, 2026
  • Environmental science. Processes & impacts
  • Simran Bamola + 3 more

This study addresses the critical issue of polycyclic aromatic hydrocarbons (PAHs) bound to total suspended particulate (TSP) in urban-industrial environments, focusing on an understudied residential area in Agra, India-a city within the heavily polluted Indo-Gangetic Plain (IGP). The research aimed to investigate seasonal variations in PAH concentrations, identify their emission sources, and assess the associated health risks. TSP samples were collected during cold weather months (CWM; January and February 2023) and hot weather months (HWM; March-May 2023) and analysed for 16 priority PAHs. The results showed notably higher TSP (349.4 ± 56.2 µg m-3) and PAH (1857.3 ng m-3) levels in CWM compared to HWM (266.5 ± 33.1 µg m-3 and 721.7 ng m-3), with high-molecular-weight PAHs dominating in CWM and 3-ring PAHs prevailing in HWM. Source apportionment using diagnostic ratios and Positive Matrix Factorization (PMF) indicated vehicular emissions, fossil fuel combustion, and industrial activities as primary contributors. Conditional Bivariate Probability Function (CBPF) analysis revealed seasonal shifts in dominant source regions-southwest in HWM and northeast in CWM-correlating with local wind patterns. Health risk assessments based on benzo(a)pyrene toxicity equivalent (BaPeq-TEQ), benzo(a)pyrene mutagenic equivalent (BaPeq-MEQ), and Incremental Lifetime Cancer Risk (ILCR) highlighted carcinogenic and mutagenic risks from BaP, BbF, and DbA via dermal and ingestion pathways. These findings underscore the need for season-specific air pollution mitigation strategies, cleaner fuels, and stricter emissions controls. The study contributes to environmental chemistry by enhancing the understanding of TSP-bound PAH behaviour, exposure pathways, and health risks in urban residential zones, thereby supporting evidence-based policymaking aligned with Sustainable Development Goals 3 and 11.

  • Research Article
  • 10.1152/jn.00567.2025
Contrast and pattern adaptation in visual cortex share a common gain control mechanism
  • May 1, 2026
  • Journal of neurophysiology
  • S Amin Moosavi + 2 more

Neuronal populations in primary visual cortex adapt both to stimulus contrast and to the probability of occurrence of visual patterns. Previous work showed that the magnitude of the population response follows a separable power-law function of contrast and stimulus probability, suggesting the existence of a shared gain mechanism. Here we ask whether a similar equivalence extends beyond response magnitude to the full distribution of activity across neurons within a trial. Across a wide range of adaptation states, we find that population responses are highly sparse and well described by a zero-inflated log-normal distribution. In this model, a fraction of neurons remain silent, while the non-zero responses follow a log-normal distribution characterized by the mean and variance of log activity. We find that both contrast and pattern adaptation produce coordinated changes in and while leaving approximately invariant. As a result, responses across all adaptation conditions collapse onto a one-dimensional manifold in parameter space. A simple linear–nonlinear population model with fixed nonlinearity and input variance reproduces these observations when adaptation acts solely by modulating the mean input to the population. Together, these findings support the idea that contrast and pattern adaptation rely on a shared gain control mechanism that shifts the operating point of cortical populations while preserving the overall structure of their response distribution.

  • Research Article
  • 10.1088/1475-7516/2026/05/029
Modeling gravitational wave bias from 3D power spectra of spectroscopic surveys
  • May 1, 2026
  • Journal of Cosmology and Astroparticle Physics
  • Dorsa Sadat Hosseini + 5 more

We present a framework for relating gravitational wave (GW) sources to the astrophysical properties of spectroscopic galaxy samples. We show how this can enable using clustering measurements of GW sources to infer the relationship between the GW sources and the astrophysical properties of their host galaxies. We accomplish this by creating mock GW catalogs from the spectroscopic Sloan Digital Sky Survey (SDSS) DR7 galaxy survey. We populate the GWs using a joint host-galaxy probability function defined over stellar mass, star formation rate (SFR), and metallicity. This probability is modeled as the product of three broken power-law distributions, each with a turnover pointmotivated by astrophysical processes governing the relation between current-day galaxy properties and binary black hole (BBH) mergers, such as galaxy quenching and BBH delay time. Given that our analysis is anchored in the specific properties and selection characteristics of the adopted galaxy sample, as well as assumptions regarding the host-galaxy probability functions and BBH merger rate prescriptions, the resulting trends should be regarded as model-dependent.Within this framework, our results show that GW bias is most sensitive to host-galaxy probability dependence on stellar mass, with increases of up to ∼𝒪(10)% relative to galaxy bias as the stellar mass pivot scale rises. We also find a notable relationship between GW bias and SFR: when the host-galaxy probability favors low-SFR galaxies, the GW bias significantly increases. In contrast, we observe no strong correlation between GW bias and metallicity. These findings suggest that the spatial clustering of GW sources is primarily driven by the stellar mass and SFR of their host galaxies and shows how GW bias measurements can inform models of the host-galaxy probability function.

  • Research Article
  • Cite Count Icon 1
  • 10.1016/j.physa.2026.131427
A multi-layer dynamic model of information propagation considering individual three-phase linear modulated behaviors
  • May 1, 2026
  • Physica A: Statistical Mechanics and its Applications
  • Yang Tian + 1 more

A multi-layer dynamic model of information propagation considering individual three-phase linear modulated behaviors

  • Research Article
  • 10.1177/14750902261429353
Assessing the impact of ship emissions on an industrial port in Chile: Insights from data monitoring and AIS analysis
  • Apr 27, 2026
  • Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment
  • Manuel José Suazo Alvarez + 4 more

This study examines the relationship between ship traffic and ambient air pollutant concentrations in Quintero Bay, Chile, an industrial coastal area characterized by intense port activity. The analysis integrates air quality measurements from the national monitoring network (SINCA) with vessel movement data derived from the AIS, combined with advanced time–frequency analysis techniques. Unlike traditional emission inventories, which aim to quantify emissions at the source, SINCA provides real-time ambient pollutant concentrations expressed in µg/m 3 and ppb. Therefore, the objective of this study is not to directly estimate ship emissions, but to evaluate how variations in maritime activity co-vary with observed pollutant levels at air quality monitoring stations. The investigation focuses on pollutants commonly associated with shipping activities, including PM 10 and PM 2.5 , NO x , SO 2 , and CO. A detailed characterization of the vessel fleet operating in the study area was performed using both static and dynamic AIS data. This included ship type classification, estimation of main engine power based on gross-tonnage models, and calculation of engine load distributions derived from AIS-reported vessel speeds. Although these parameters allow the estimation of emission factors, the present work emphasizes identifying temporal associations between ship movements and ambient pollutant concentrations rather than quantifying emissions. Additionally, pollution roses and Conditional Probability Functions (CPF) were used to evaluate the directional origin of high-concentration episodes in relation to prevailing wind conditions. The results show that several episodes of elevated NO x , SO 2 , and PM 10 concentrations exhibit significant coherence with ship activity, particularly at daily time scales influenced by local meteorology. Among the analyzed pollutants, PM 10 displays the strongest and most recurrent association with maritime traffic, highlighting the influence of port operations on air quality in Quintero Bay.

  • Research Article
  • 10.3329/ijss.v26i1.88849
Hook Method of Integration by Parts and its Applications to Probability Theory
  • Apr 21, 2026
  • International Journal of Statistical Sciences
  • Anwar H Joarder

Integration of the product of two functions involves steps that are often messy. Tabular methods available in online or in the literature are not that transparent. We present it in a way that the repeated integrals yield a series of parallel lines unless you stop at any step, and the last step yields a hook, and hence the name hook method. We apply it to calculate higher order moments and cumulative probability or survival functions of an exponential random variable related to service times. IJSS, Vol. 26(1), March, 2026, pp 107-118

  • Research Article
  • 10.64898/2026.04.20.719455
Unlocking a flexible set of phylogenetic models for discrete and continuous trait evolution using discretized stochastic diffusion
  • Apr 21, 2026
  • bioRxiv
  • Liam J Revell + 8 more

The practical utility of many modern phylogenetic comparative methods can depend on how accurately mathematical models capture the evolutionary process of traits. Boucher and Démery (2016) described a new quantitative trait model, Brownian motion with reflective limits, that they anticipated might be of use in testing hypotheses about a particular sort of constraint on phenotypic character evolution. Since their analytic solution for the probability function under this bounded evolutionary scenario was not practical to evaluate for reasonably-sized trees, Boucher and Démery (2016) also identified a creative technique for computing the likelihood of their model. The basis of this methodology derives from the convergence of an equal-rates, symmetric, ordered Markov chain and continuous stochastic diffusion in the limit as the number of steps in our chain goes to (or, alternatively, as their widths decrease towards zero). We refer to this convergence in the limit as the discretized diffusion approximation or (more compactly) the discrete approximation. We realized that this discrete approximation of Boucher and Démery (2016) unlocked a number of additional models for the phylogenetic comparative analysis of discrete and continuous trait data, and we explore several of these in the present article. Specifically, we examine application of this discretized diffusion approximation to the threshold model from evolutionary quantitative genetics, to a new “semi-threshold” trait evolution model, to a joint model of discrete and continuous traits in which the discrete trait influences the rate of evolution of our continuous character, as well as a model where precisely the converse is true, and to a discrete character dependent multi-trend trended continuous trait evolution model. We conclude with some context for the origins of our article and discussion of other possible applications of this powerful approach.

  • Research Article
  • 10.1007/s10910-026-01780-x
Improving operator splitting and effective reaction probability for a reactive-step based molecular dynamics workflow
  • Apr 21, 2026
  • Journal of Mathematical Chemistry
  • Souvik Mitra + 2 more

Abstract Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods. However, due to fixed force-field parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a simple approach that incorporates quantum reactions by periodically halting the MD simulation and allowing the possibility for reactions at each halt, based on a Poisson-type reaction probability. But, this simple approach cannot capture the simultaneous involvement of diffusion and reaction processes, and because the reaction probability does not include the influence of the diffusion step, errors can be introduced, especially when the diffusion process is not significantly slower than the reaction process. In this work, the efficiency of the RSMD model is increased by reducing these errors and by addressing the influence of the diffusion process on the reaction probability. To reduce these errors, we modify the RSMD mathematical framework by replacing the Trotter splitting employed in previous works with the Strang splitting scheme. To implement these Strang schemes in MD simulations and to scrutinize their validity, we introduce mathematical models involving three and four states, which correspond to two common reaction scenarios: association-dissociation reactions and homogeneous charge transfer reactions, respectively in the presence of diffusion processes. Using these mathematical models, effective reaction probability functions are derived for various diffusion limits, for example, when diffusion processes are extremely fast or extremely slow compared to the reaction processes. All the derived reaction probability functions, in combination with appropriate Strang schemes, are validated for various diffusion regimes with respect to the reaction time scale.

  • Research Article
  • 10.1007/s00184-026-01030-9
Computing marginal eigenvalue distributions for the Gaussian and Laguerre orthogonal ensembles
  • Apr 20, 2026
  • Metrika
  • Peter J Forrester + 2 more

Abstract The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix theory, and the marginal eigenvalue distributions are basic observable quantities often relevant to applications. Notwithstanding a long history, a formulation providing high precision numerical evaluations for N large enough to probe asymptotic regimes, has not been provided. An exception is for the largest eigenvalue, where there is a formalism due to Chiani which uses a combination of a formulation as a positive real valued Pfaffian, and a recursive computation of the matrix elements. We augment this strategy by introducing a generating function for the conditioned gap probabilities. A finite Fourier series approach is then used to extract the sequence of marginal eigenvalue distributions as a linear combination of complex valued Pfaffians, with the latter then evaluated using an efficient numerical procedure available in the literature due to Wimmer. Applications are given to illustrating various asymptotic formulas, local central limit theorems, and central limit theorems, as well as to probing finite size corrections. Further, our data indicates that the mean values of the marginal distributions interlace with the zeros of the Hermite polynomial (Gaussian ensemble) and a particular Laguerre polynomial (Laguerre ensemble).

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • .
  • .
  • .
  • 10
  • 1
  • 2
  • 3
  • 4
  • 5

Popular topics

  • Latest Artificial Intelligence papers
  • Latest Nursing papers
  • Latest Psychology Research papers
  • Latest Sociology Research papers
  • Latest Business Research papers
  • Latest Marketing Research papers
  • Latest Social Research papers
  • Latest Education Research papers
  • Latest Accounting Research papers
  • Latest Mental Health papers
  • Latest Economics papers
  • Latest Education Research papers
  • Latest Climate Change Research papers
  • Latest Mathematics Research papers

Most cited papers

  • Most cited Artificial Intelligence papers
  • Most cited Nursing papers
  • Most cited Psychology Research papers
  • Most cited Sociology Research papers
  • Most cited Business Research papers
  • Most cited Marketing Research papers
  • Most cited Social Research papers
  • Most cited Education Research papers
  • Most cited Accounting Research papers
  • Most cited Mental Health papers
  • Most cited Economics papers
  • Most cited Education Research papers
  • Most cited Climate Change Research papers
  • Most cited Mathematics Research papers

Latest papers from journals

  • Scientific Reports latest papers
  • PLOS ONE latest papers
  • Journal of Clinical Oncology latest papers
  • Nature Communications latest papers
  • BMC Geriatrics latest papers
  • Science of The Total Environment latest papers
  • Medical Physics latest papers
  • Cureus latest papers
  • Cancer Research latest papers
  • Chemosphere latest papers
  • International Journal of Advanced Research in Science latest papers
  • Communication and Technology latest papers

Latest papers from institutions

  • Latest research from French National Centre for Scientific Research
  • Latest research from Chinese Academy of Sciences
  • Latest research from Harvard University
  • Latest research from University of Toronto
  • Latest research from University of Michigan
  • Latest research from University College London
  • Latest research from Stanford University
  • Latest research from The University of Tokyo
  • Latest research from Johns Hopkins University
  • Latest research from University of Washington
  • Latest research from University of Oxford
  • Latest research from University of Cambridge

Popular Collections

  • Research on Reduced Inequalities
  • Research on No Poverty
  • Research on Gender Equality
  • Research on Peace Justice & Strong Institutions
  • Research on Affordable & Clean Energy
  • Research on Quality Education
  • Research on Clean Water & Sanitation
  • Research on COVID-19
  • Research on Monkeypox
  • Research on Medical Specialties
  • Research on Climate Justice
Discovery logo
FacebookTwitterLinkedinInstagram

Download the FREE App

  • Play store Link
  • App store Link
  • Scan QR code to download FREE App

    Scan to download FREE App

  • Google PlayApp Store
FacebookTwitterTwitterInstagram
  • Universities & Institutions
  • Publishers
  • R Discovery PrimeNew
  • Ask R Discovery
  • Blog
  • Accessibility
  • Topics
  • Journals
  • Open Access Papers
  • Year-wise Publications
  • Recently published papers
  • Pre prints
  • Questions
  • FAQs
  • Contact us
Lead the way for us

Your insights are needed to transform us into a better research content provider for researchers.

Share your feedback here.

FacebookTwitterLinkedinInstagram
Cactus Communications logo

Copyright 2026 Cactus Communications. All rights reserved.

Privacy PolicyCookies PolicyTerms of UseCareers