Two-point Correlation Function Research Articles

Halo Asymmetry in the Modeling of Galaxy Clustering

Conventional studies of galaxy clustering within the framework of halo models typically assume that the density profile of all dark matter halos can be approximated by the Navarro–Frenk–White (NFW) spherically symmetric profile. However, both modern N-body simulations and observational data suggest that most halos are either oblate or prolate, and almost never spherical. In this paper we present a modified model of the galaxy correlation function. In addition to the five “classical” halo occupation distribution (HOD) parameters proposed by Zheng et al., it includes an additional free parameter ϕ in the modified NFW density profile describing the asymmetry of the host dark matter halo. Using a subhalo abundance matching model, we populate galaxies within BolshoiP N-body simulations. We compute the projected two-point correlation function w p (r p ) for six stellar-mass volume-limited galaxy samples. We fit our model to the results and then compare the best-fit asymmetry parameter ϕ (and other halo parameters) to the asymmetry of dark matter halos measured directly from the simulations and find that they agree within 1σ. We then fit our model to the w p (r p ) results from Zehavi et al. and compare halo parameters. We show that our model accurately retrieves the halo asymmetry and other halo parameters. Additionally, we find 2%–6% differences between the halo masses ( logMmin and logM 1) estimated by our model and those estimated by “classical” HOD models. The model proposed in this paper can serve as an alternative to multiparameter HOD models, since it can be used for relatively small samples of galaxies.

Cosmological constraints from density-split clustering in the BOSS CMASS galaxy sample

Abstract We present a clustering analysis of the BOSS DR12 CMASS galaxy sample, combining measurements of the galaxy two-point correlation function and density-split clustering down to a scale of 1 h−1 Mpc. Our theoretical framework is based on emulators trained on high-fidelity mock galaxy catalogues that forward model the cosmological dependence of the clustering statistics within an extended-ΛCDM framework, including redshift-space and Alcock-Paczynski distortions. Our base-ΛCDM analysis finds ωcdm = 0.1201 ± 0.0022, σ8 = 0.792 ± 0.034, and ns = 0.970 ± 0.018, corresponding to fσ8 = 0.462 ± 0.020 at z ≈ 0.525, which is in agreement with Planck 2018 predictions and various clustering studies in the literature. We test single-parameter extensions to base-ΛCDM, varying the running of the spectral index, the dark energy equation of state, and the density of massless relic neutrinos, finding no compelling evidence for deviations from the base model. We model the galaxy-halo connection using a halo occupation distribution framework, finding signatures of environment-based assembly bias in the data. We validate our pipeline against mock catalogues that match the clustering and selection properties of CMASS, showing that we can recover unbiased cosmological constraints even with a volume 84 times larger than the one used in this study.

Accurate Memory Kernel Extraction from Discretized Time-Series Data.

Memory effects emerge as a fundamental consequence of dimensionality reduction when low-dimensional observables are used to describe the dynamics of complex many-body systems. In the context of molecular dynamics (MD) data analysis, accounting for memory effects using the framework of the generalized Langevin equation (GLE) has proven efficient, accurate, and insightful, particularly when working with high-resolution time series data. However, in experimental systems, high-resolution data are often unavailable, raising questions about the impact of the data resolution on the estimated GLE parameters. This study demonstrates that direct memory extraction from time series data remains accurate when the discretization time is below the memory time. To obtain memory functions reliably, even when the discretization time exceeds the memory time, we introduce a Gaussian Process Optimization (GPO) scheme. This scheme minimizes the deviation of discretized two-point correlation functions between time series data and GLE simulations and is able to estimate accurate memory kernels as long as the discretization time stays below the longest time scale in the data, typically the barrier crossing time.

Correlation functions in the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{TsT}}/T\\overline{T }$$\\end{document} correspondence

We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS3 × \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} with NS-NS flux and a single-trace \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T\\overline{T }$$\\end{document} deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T\\overline{T }$$\\end{document} deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing h with \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h+2\\frac{\\widetilde{\\lambda }}{w}p\\overline{p }$$\\end{document}, where h is the spacetime conformal weight, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{\\lambda }$$\\end{document} is a deformation parameter, p and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{p }$$\\end{document} are the momenta, and w labels the twisted sectors in the deformed symmetric product. At w = 1, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T\\overline{T }$$\\end{document} deformed CFT derived in [1]. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{TsT}}/T\\overline{T }$$\\end{document} correspondence.

Generation of realistic input parameters for simulating atmospheric point-spread functions at astronomical observatories

High-fidelity simulated astronomical images are an important tool in developing and measuring the performance of image-processing algorithms, particularly for high precision measurements of cosmic shear – correlated distortions of images of distant galaxies due to weak gravitational lensing caused by the large-scale mass distribution in the Universe. For unbiased measurements of cosmic shear, all other sources of correlated image distortions must be modeled or removed. One such source is the correlated blurring of images due to optical turbulence in the atmosphere, which dominates the point-spread function (PSF) for ground-based instruments. In this work, we leverage data from weather forecasting models to produce wind speeds and directions, and turbulence parameters, that are realistically correlated with altitude. To study the resulting correlations in the size and shape of the PSF, we generate simulated images of the PSF across a ~10 square-degree field of view – the size of the camera focal plane for the Vera C. Rubin Observatory in Chile – using weather data and historical seeing for a geographic location near the Observatory. We make quantitative predictions for two-point correlation functions (2PCF) that are used in analyses of cosmic shear. We observe a strong anisotropy in the two-dimensional 2PCF, which is expected based on observations in real images, and study the dependence of the orientation of the anisotropy on dominant wind directions near the ground and at higher altitudes. The code repository for producing the correlated weather parameters for input to simulations (psf-weather-station) is public at https://github.com/LSSTDESC/psf-weather-station (https://github.com/LSSTDESC/psf-weather-station)

Fast forward modelling of galaxy spatial and statistical distributions

A forward modelling approach provides simple, fast and realistic simulations of galaxy surveys, without a complex underlying model. For this purpose, galaxy clustering needs to be simulated accurately, both for the usage of clustering as its own probe and to control systematics. We present a forward model to simulate galaxy surveys, where we extend the Ultra-Fast Image Generator to include galaxy clustering. We use the distribution functions of the galaxy properties, derived from a forward model adjusted to observations. This population model jointly describes the luminosity functions, sizes, ellipticities, SEDs and apparent magnitudes. To simulate the positions of galaxies, we then use a two-parameter relation between galaxies and halos with Subhalo Abundance Matching (SHAM). We simulate the halos and subhalos using the fast PINOCCHIO code, and a method to extract the surviving subhalos from the merger history. Our simulations contain a red and a blue galaxy population, for which we build a SHAM model based on star formation quenching. For central galaxies, mass quenching is controlled with the parameter Mlimit, with blue galaxies residing in smaller halos. For satellite galaxies, environmental quenching is implemented with the parameter tquench, where blue galaxies occupy only recently merged subhalos. We build and test our model by comparing to imaging data from the Dark Energy Survey Year 1. To ensure completeness in our simulations, we consider the brightest galaxies with i < 20. We find statistical agreement between our simulations and the data for two-point correlation functions on medium to large scales. Our model provides constraints on the two SHAM parameters Mlimit and tquench and offers great prospects for the quick generation of galaxy mock catalogues, optimized to agree with observations.

Artificial neural network prediction of transverse modulus in humid conditions for randomly distributed unidirectional fibre reinforced composites: A micromechanics approach

This paper proposes an innovative micromechanics-based artificial neural network (ANN) method to efficiently investigate the transverse modulus of unidirectional fibre/epoxy composites under humid conditions. In this research, a novel approach is developed to establish relations between the geometrical, mechanical, and environmental properties of the microstructure and the material’s performance under transverse tension. A framework is developed to artificially generate periodic representative volume elements (RVEs) while taking into account the interphase region between fibre and matrix. The RVEs are analysed by the finite element method to obtain the transverse moduli of composites. Two-point correlation functions and principal component analysis techniques are applied to extract and compress statistical information from microstructure images. A database establishment framework is developed to create three batches of data with 1000, 2000, and 3000 sizes. An ANN-based prediction framework is developed by integrating 10-fold cross-validation and Bayesian optimisation to optimise the neural network architecture and establish an efficient structure-property linkage under the influence of humid conditions. The prediction results demonstrate the efficiency of ANN in mapping microstructural data to an effective transverse modulus. A parametric study by ANN reveals the role of microstructure geometrical features and humid environmental parameters on the transverse performance of the composite.

Non-equilibrium Dynamics of Vortices in Two-Dimensional Quantum Gases: Determining the Dynamical Scaling Region Using the Mahalanobis Distance

AbstractWhen a system undergoes a rapid quench from a disordered to an ordered phase, it does not order instantly but instead relaxes towards equilibrium over time. During this relaxation, the dynamical scaling hypothesis predicts that the length scale of ordered regions increases, with later patterns statistically similar to earlier ones except for a change in global scale. Quantum gases are one of many systems in which such out of equilibrium behaviour is predicted to occur. Here, we present a method for systematically testing when dynamical scaling is taking place, by quantifying the similarity of the rescaled two-point correlation function over time using the Mahalanobis distance. Data on the velocity field of a two-dimensional quantum fluid, generated from point vortex simulations, are used to illustrate the application of this method.

Do galaxy mergers prefer under-dense environments?

Galaxy mergers play a crucial role in galaxy evolution. However, the correlation between mergers and the local environment of galaxies is not fully understood. We aim to address the question of whether galaxy mergers prefer denser or less dense environments by quantifying the spatial clustering of mergers and non-mergers. We use two different indicators to classify mergers and non-mergers -- classification based on a deep learning technique ($f$) and non-parametric measures of galaxy morphology, Gini-$M_ $ ($g$). We used a set of galaxy samples in the redshift range $0.1 &lt; z &lt; 0.15$ from the Galaxy and Mass Assembly (GAMA) survey with a stellar mass cut of $ star M sun &gt; 9.5$. We measured and compared the two-point correlation function (2pCF) of the mergers and non-mergers classified using the two merger indicators $f$ and $g$. We measured the marked correlation function (MCF), in which the galaxies were weighted by $f$ to probe the environmental dependence of galaxy mergers. We do not observe a statistically significant difference between the clustering strengths of mergers and non-mergers obtained using 2pCF. However, using the MCF measurements with $f$ as a mark, we observe an anti-correlation between the likelihood of a galaxy being a merger and its environment. Our results emphasise the advantage of MCF over 2pCF in probing the environmental correlations. Based on the MCF measurements, we conclude that the galaxy mergers prefer to occur in the under-dense environments on scales $&gt; 50 \ kpc $ of the large-scale structure (LSS). We attribute this observation to the high relative velocities of galaxies in the densest environments that prevent them from merging.

Euclid preparation

Aims. We validate a semi-analytical model for the covariance of the real-space two-point correlation function of galaxy clusters. Methods. Using 1000 PINOCCHIO light cones mimicking the expected Euclid sample of galaxy clusters, we calibrated a simple model to accurately describe the clustering covariance. Then, we used this model to quantify the likelihood-analysis response to variations in the covariance, and we investigated the impact of a cosmology-dependent matrix at the level of statistics expected for the Euclid survey of galaxy clusters. Results. We find that a Gaussian model with Poissonian shot-noise does not correctly predict the covariance of the two-point correlation function of galaxy clusters. By introducing a few additional parameters fitted from simulations, the proposed model reproduces the numerical covariance with an accuracy of 10%, with differences of about 5% on the figure of merit of the cosmological parameters Ωm and σ8. We also find that the covariance contains additional valuable information that is not present in the mean value, and the constraining power of cluster clustering can improve significantly when its cosmology dependence is accounted for. Finally, we find that the cosmological figure of merit can be further improved when mass binning is taken into account. Our results have significant implications for the derivation of cosmological constraints from the two-point clustering statistics of the Euclid survey of galaxy clusters.

Topological bias: how haloes trace structural patterns in the cosmic web

ABSTRACT We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalize clustering up to the second-order correlation function and use our systematic topological analysis to correlate local information and properties of haloes with their multiscale geometrical environment of the cosmic web (elongated filamentary bridges and sheetlike walls). We capture the multiscale topology traced by the halo distribution through filtrations of the corresponding Delaunay tessellation. The resulting nested alpha shapes are sensitive to the local density, perfectly outline the local geometry, and contain the complete information on the multiscale topology. We find a remarkable linear relationship between halo masses and topology: haloes of different mass trace environments with different topological signature. This is a topological bias, an environmental structure bias independent of the halo clustering bias associated with the two-point correlation function. This mass-dependent linear scaling relation allows us to take clustering into account and determine the overall connectivity from a limited sample of galaxies. The presence of topological bias has major implications for the study of voids and filaments in the observed distribution of galaxies. The (infra)structure and shape of these key cosmic web components will strongly depend on the underlying galaxy sample. Their use as cosmological probes, with their properties influenced by cosmological parameters, will have to account for the subtleties of topological bias. This is of particular relevance with the large upcoming galaxy surveys such as DESI, Euclid, and the Vera Rubin telescope surveys.

Euclid Preparation. XL. Impact of magnification on spectroscopic galaxy clustering

In this paper we investigate the impact of lensing magnification on the analysis of spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering . We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored . We considered two cosmological analyses: (i) a full-shape analysis based on the Lambda cold dark matter (CDM) model and its extension $ and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code . For a Lambda CDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4--0.7 standard deviations, while for a $ dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to $1.2$ standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead

Dual symplectic classical circuits: An exactly solvable model of many-body chaos

We propose a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of symplectic dynamics in two orthogonal (time and space) directions. In close analogy with quantum dual-unitary circuits, we prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. The dynamical correlations are exactly computable in terms of a one-site Markov transfer operator, which is generally of infinite dimensionality. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain. Remarkably, expressing these models in the form of a composition of rotations leads to a transfer operator with a block diagonal form in the basis of spherical harmonics. This allows us to obtain analytical predictions for simple local observables. We demonstrate the validity of our theory by comparison with Monte Carlo simulations, displaying excellent agreement with the latter for a choice of observables.

Holographic two-point functions in medium

In this paper, we study two-point correlation function in a medium composed of two kinds of matter, which is the dual of a three-dimensional generalized p-brane gas geometry. Following the holographic prescription, we calculate temporal and spatial two-point functions in the medium. In general, the screening effect of the medium makes two-point functions decreases more rapidly than the CFTs two-point function. In the extremal limit, however, we find that a temporal two-point function is still conformal. This indicates that a two-dimensional UV CFT flows into a one-dimensional quantum mechanics in the IR limit. This is consistent with the fact that the near horizon geometry in the extremal limit reduces to AdS2. We also investigate holographic mutual information representing the correlation between two subsystems. We show that a critical distance in the IR region, where the mutual information vanishes, leads to a similar behavior to the correlation length of a two-point function.

Rigorous Screened Interactions for Realistic Correlated Electron Systems.

We derive a widely applicable first-principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous two-point correlation functions in a chosen model space at the level of the random phase approximation, improving upon the traditional uncontrolled static approximations. Applied to screened interactions within a quantum embedding framework, we demonstrate these faithfully describe the relaxation of local subspaces via downfolding high-energy physics in molecular systems, as well as enabling a systematically improvable description of the long-range plasmonic contributions in extended graphene.

Cosmological evolution of metallicity correlation functions from the Auriga simulations

ABSTRACT We study the cosmological evolution of the two-point correlation functions of galactic gas-phase metal distributions using the 28 simulated galaxies from the Auriga Project. Using mock observations of the z = 0 snapshots to mimic our past work, we show that the correlation functions of the simulated mock observations are well matched to the correlation functions measured from local galaxy surveys. This comparison suggests that the simulations capture the processes important for determining metal correlation lengths, the key parameter in metallicity correlation functions. We investigate the evolution of metallicity correlations over cosmic time using the true simulation data, showing that individual galaxies undergo no significant systematic evolution in their metal correlation functions from z ∼ 3 to today. In addition, the fluctuations in metal correlation length are correlated with but lag ahead fluctuations in star formation rate. This suggests that re-arrangement of metals within galaxies occurs at a higher cadence than star formation activity, and is more sensitive to the changes of environment, such as galaxy mergers, gas inflows/outflows, and fly-bys.

A new test of gravity – II. Application of marked correlation functions to luminous red galaxy samples

ABSTRACT We apply the marked correlation function test proposed by Armijo et al. (Paper I) to samples of luminous red galaxies (LRGs) from the final data release of the Sloan Digital Sky Survey (SDSS) III. The test assigns a density-dependent mark to galaxies in the estimation of the projected marked correlation function. Two gravity models are compared: general relativity (GR) and $f(R)$ gravity. We build mock catalogues which, by construction, reproduce the measured galaxy number density and two-point correlation function of the LRG samples, using the halo occupation distribution model (HOD). A range of HOD models give acceptable fits to the observational constraints, and this uncertainty is fed through to the error in the predicted marked correlation functions. The uncertainty from the HOD modelling is comparable to the sample variance for the SDSS-III LRG samples. Our analysis shows that current galaxy catalogues are too small for the test to distinguish a popular $f(R)$ model from GR. However, upcoming surveys with a better measured galaxy number density and smaller errors on the two-point correlation function, or a better understanding of galaxy formation, may allow our method to distinguish between viable gravity models.

Interface fluctuations associated with split Fermi seas

We consider the asymptotic behaviour of a family of unidimensional lattice fermion models, which are in exact correspondence with certain probability laws on partitions and on unitary matrices. These models exhibit limit shapes, and in the case where the bulk of these shapes are described by analytic functions, the fluctuations around their interfaces have been shown to follow a universal Tracy–Widom distribution or its higher-order analogue. Non-differentiable bulk limit shape functions arise when a gap appears in some quantum numbers of the model, in other words when the Fermi sea is split. We show that split Fermi seas give rise to new interface fluctuations, governed by integer powers of universal distributions. This breakdown in universality is analogous to the behaviour of a random Hermitian matrix when the support of its limiting eigenvalue distribution has multiple cuts, with oscillations appearing in the limit of the two-point correlation function. We show that when the Fermi sea is split in the lattice fermion model, there are multiple cuts in the eigenvalue support of the corresponding unitary matrix model.

Cosmological constraints from the abundance, weak lensing, and clustering of galaxy clusters: Application to the SDSS

Aims. The clustering of galaxy clusters is a powerful cosmological tool. When it is combined with other cosmological observables, it can help to resolve parameter degeneracies and improve constraints, especially on Ωm and σ8. We aim to demonstrate its potential in constraining cosmological parameters and scaling relations when combined with cluster counts and weak-lensing mass information. As a case study, we use the redMaPPer cluster catalog derived from the Sloan Digital Sky Survey (SDSS). Methods. We extended a previous analysis of the number counts and weak-lensing signal by the two-point correlation function. We derived cosmological and scaling relation posteriors for all possible combinations of the three observables to assess their constraining power, parameter degeneracies, and possible internal tensions. Results. We find no evidence for tensions between the three data sets we analyzed. We demonstrate that the constraining power of the sample can be greatly improved by including the clustering statistics because this can break the Ωm − σ8 degeneracy that is characteristic of cluster abundance studies. In particular, for a flat ΛCDM model with massive neutrinos, we obtain Ωm = 0.28 ± 0.03 and σ8 = 0.82 ± 0.05, which is an improvement of 33% and 50% compared to the posteriors derived by combining cluster abundance and weak-lensing analyses. Our results are consistent with cosmological posteriors from other cluster surveys, and also with Planck results for the cosmic microwave background (CMB) and DES-Y3 galaxy clustering and weak-lensing analysis.

Using the Two-point Correlation Function to Understand the Assembly Histories of Milky Way–like Galaxies

The two-point correlation function (2PCF) is a powerful statistical tool to measure galaxy clustering. Although 2PCF has also been used to study the clustering of stars on subparsec to kiloparsec scales, its physical implication is not clear. In this study, we use the Illustris-TNG50 simulation to study the connection between the 2PCF of accreted halo stars and the assembly histories of Milky Way-mass galaxies. We find, in general, that the 2PCF signal increases with the increase in galactocentric radii, r, and with the decrease in the pair separations. Galaxies that assemble late on average have stronger 2PCF signals. With z 1/4, z 1/2, and z 3/4 defined as the redshifts when galaxies accreted one-fourth, half, and three-fourths of their ex situ stellar mass today, we find they all show the strongest correlations with the 2PCF signals at r < ∼ 0.2R 200. z 3/4 shows the strongest correlations than those of z 1/4 or z 1/2. However, the correlations have large scatters. The 2PCFs in the velocity space show weaker correlations with the galaxy formation times within ∼0.35R 200 than real-space 2PCFs, and the scatter is considerably large. Both the real- and velocity-space 2PCFs correlate with the assembly histories of the host dark matter halos as well. Within 0.3R 200, the real-space 2PCF shows stronger correlations with the galaxy formation histories than with the halo formation histories. We conclude that it is difficult to use 2PCF alone to precisely predict the formation times or assembly histories of galaxies.