Limit Laws Research Articles

The relative effectiveness of law enforcement policies aimed at reducing illegal trade: Evidence from laboratory markets.

Despite recent emphasis and implementation of national and international anti-money laundering policies, illegal product markets, and their associated illicit profit remain a global problem. In addition to law enforcement aimed at reducing money-laundering, enforcement also takes place during (1) the production (e.g. crop eradication) and (2) sale (e.g. seizure of products during transportation that interrupts buyer and seller transactions) of the illegal product. Since funds for enforcement come from limited budgets, understanding where in this production-trade-laundering cycle law enforcement is most impactful becomes a global question. Using laboratory experimental markets and a seizure rate of 20%, we find that law enforcement focused on seizing laundered profits does little to reduce illegal market activity when compared to no law enforcement, suggesting that focusing law enforcement on money laundering will likely be ineffective at reducing crime. Results further show the amount of illicit trade is nearly 32% lower when law enforcement is focused at the point of sale, and there may be additional economic incentives that reduce illicit trade in the long run when compared to no law enforcement. Enforcement at the point of production also reduces market activity, but not as effectively as enforcement at the point of sale. Lastly, the empirical findings deviate from equilibrium predictions, suggesting law enforcement policy based on theory alone may lead to inefficient allocation of limited law enforcement resources.

Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions

We study Bessel and Dunkl processes (Xt,k)t≥0 on RN with possibly multivariate coupling constants k≥0. These processes describe interacting particle systems of Calogero–Moser–Sutherland type with N particles. For the root systems AN−1 and BN these Bessel processes are related with β-Hermite and β-Laguerre ensembles. Moreover, for the frozen case k=∞, these processes degenerate to deterministic or pure jump processes.We use the generators for Bessel and Dunkl processes of types A and B and derive analogues of Wigner’s semicircle and Marchenko–Pastur limit laws for N→∞ for the empirical distributions of the particles with arbitrary initial empirical distributions by using free convolutions. In particular, for Dunkl processes of type B new non-symmetric semicircle-type limit distributions on R appear. Our results imply that the form of the limiting measures is already completely determined by the frozen processes. Moreover, in the frozen cases, our approach leads to a new simple proof of the semicircle and Marchenko–Pastur limit laws for the empirical measures of the zeros of Hermite and Laguerre polynomials respectively.

State firearm laws and nonfatal firearm injury-related inpatient hospitalizations: A nationwide panel study.

Firearm injury remains a major cause of morbidity and mortality in the United States. Because of prior lack of comprehensive data sources, there is a paucity of literature on nonfatal firearm injury. Associations have previously been shown between state-level firearm laws and firearm fatalities, but few studies have examined the effects of these laws on nonfatal firearm hospitalization rates. Our objective was to examine the relationship between state firearm laws and firearm injury-related hospitalization rates across all 50 states over a 17-year period. In this panel study design, we used fixed effects multivariate regression models to analyze the relationship between 12 laws and firearm state-level injury-related hospitalization rates from 2000 to 2016 using the RAND Corporation Inpatient Hospitalizations for Firearm Injury Database. We used difference-in-differences to determine the impact of law passage in a given state compared with those states without the law, controlling for state-level covariates. The main outcome measure was the change in annual firearm injury-related inpatient hospitalization rates after passage or repeal of a state-level firearm law. Examining each law individually, passage of violent misdemeanor, permitting, firearm removal from domestic violence offenders, and 10-round limit laws were associated with significant firearm injury-related hospitalization rate reductions. Examining multiple laws in the same model, passage of violent misdemeanor laws was associated with a 19.9% (confidence interval, 11.6%-27.4%) reduction, and removal of firearms from domestic violence offenders was associated with a 17.0% (confidence interval, 9.9%-23.6%) reduction in hospitalization rates. State laws related to preventing violent offenders from possessing firearms are associated with firearm injury-related hospitalization rate reductions. Given significant physical, mental, and social burdens of nonfatal firearm injury, determining the efficacy of firearm-related policy is critical to violence and injury prevention efforts. Prognostic and Epidemiologic; Level IV.

Asymptotic analysis of a storage allocation model with finite capacity: Marginal and conditional distributions

We consider a dynamic storage allocation model with a finite number of storage spaces. There are m primary spaces and R secondary spaces. Items arrive according to a Poisson process and an arriving item takes the lowest ranked available space. Each item occupies a storage space for an exponentially distributed amount of time. Letting N1 and N2 denote the numbers of occupied primary and secondary spaces, we examine the steady-state marginal distribution of N2 and derive various conditional limit laws for Prob[N1=k∣N2=r]. The joint process (N1,N2) behaves as a random walk in a lattice rectangle. We scale the storage capacities m and R to be large and study the problem asymptotically as the Poisson arrival rate λ becomes large. We previously derived detailed asymptotic results for the joint distribution Prob[N1=k,N2=r] and we use these results here to study the marginal and conditional distributions.

Electromagnetic characterization of the environment. An Italian experience and the “mapping” method

The “mapping” method is our original approach to obtain a more reliable electromagnetic characterization of the environment than the usual point-type method; and it is proposed after having tested it over time in various characterization campaigns. Specially with its improvement by resorting to GIS (Geographic Information Systems), the “mapping” method provides a more accurate report, closer to the real condition, to the Municipality committed to verifying compliance with the law of the emission exposure limits of radio transmitting stations and antennas installed in its borders, as well as to citizens concerned about this exposure; an indispensable basis for a possible more detailed health picture. In one campaign a check of the influence of electromagnetic field (EMF) on human cells has been realized. In the last campaigns a simpler representation, always of cartographic type, has been used to make easier citizens the understanding of the electromagnetic situation in their territory: the “pertinent lobes” model.

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Extreme statistics of the excitations in the random transverse Ising chain

In random quantum magnets, like the random transverse Ising chain, low energy excitations are localized in rare regions and there are only weak correlations between them. It is an open question whether these correlations are relevant in the sense of the renormalization group. To answer this question, we calculate the distribution of the excitation energy of the random transverse Ising chain in the disordered Griffiths phase with high numerical precision by the strong disorder renormalization group method and---for shorter chains---by free-fermion techniques. Asymptotically, the two methods give identical results, which are well fitted by the Fr\'echet limit law of the extremes of independent and identically distributed random numbers. Considering the finite size corrections, the two numerical methods give very similar results, but these differ from the correction term for uncorrelated random variables, indicating that the weak correlations between low-energy excitations in random quantum magnets are relevant.

Distributions for Nonsymmetric Monotone and Weakly Monotone Position Operators

We study the vacuum distribution, under an appropriate scaling, of a family of partial sums of nonsymmetric position operators on weakly monotone and monotone Fock spaces, respectively. We preliminary treat the case of weakly monotone Fock space, and show that any single operator has the vacuum law belonging to the free Meixner class. After establishing some relations between the combinatorics of Motzkin and Riordan paths, we give a recursive formula for the vacuum moments of the law of any finite sum. Since the operators are monotone independent, the distribution is the monotone convolution of the free Meixner law above. We also investigate the asymptotic measure for these sums, which can be seen as “Poisson type” limit law. It turns out to belong to the free Meixner class, with an atomic and an absolutely continuous part (w.r.t. the Lebesgue measure). Finally, we briefly apply analogous considerations to the case of monotone Fock space.

Association of State Gestational Age Limit Abortion Laws With Infant Mortality

A growing number of state legislatures have passed laws that restrict access to abortion care after a specified gestational age (gestational age limit laws). The impact of these laws on maternal and child population health outcomes and inequities is unknown. The objective of this study is to determine whether states that implement gestational age limit laws experience subsequent changes in rates of infant mortality. Using U.S. population‒based data from the National Center for Health Statistics Linked Infant Birth-Death Files (2005-2017), difference-in-differences models were estimated using multivariable linear regressions to compare the trends in infant mortality (all-cause and cause-specific rates) in states with gestational age limit laws with the trends in states without such laws. Models stratified by maternal racial/ethnic group explored racial heterogeneity in the law's impact. Data were analyzed in 2020. This study included 16,232,133 births in states that enacted a gestation age limit abortion law and 36,472,309 births in states that did not from 2005 to 2017. In difference-in-difference analyses, gestational age limit laws were associated with 0.23 excess infant deaths per 1,000 live births (95% CI=0.09, 0.37, p<0.01). In cause-specific analyses, gestational age limit laws were associated with 0.10 additional infant deaths owing to congenital anomalies per 1,000 live births (95% CI=0.03, 0.17, p=0.01). Associations between gestational age limit laws and infant mortality in models stratified by maternal racial/ethnic group were not statistically significant. On the basis of data from 2005 to 2017, states that enacted gestational age limit abortion laws subsequently experienced increased infant mortality rates.

The Kurdistan Worker’s Party (PKK) in London: Countering Overseas Terrorist Financing and Support with “Nudge” and Situational Approaches

ABSTRACT Overseas diasporas have long been exploited by terrorist organisations seeking funding and support from areas beyond their operation. The Kurdistan Worker’s Party (PKK), active in south-eastern Turkey, is no exception and maintains a significant international presence. This paper uses seventy-three survey responses and thirteen interviews amongst London’s Turkish and Kurdish diaspora to provide an original and comprehensive insight into the PKK’s overseas operations, including their offending patterns, methods, hotspots, offender/victim profiles and existing countermeasures. Respondents were also consulted on new community-based prevention measures designed to address limited law enforcement responses and the laissez-faire approaches of diaspora host countries. This strategy, which combines crime science and behavioural economic theories, consists of Clarke’s “Situational Crime Prevention” theory and Thaler and Sunstein’s “Nudge” theory (SCP+N). The results indicate that the PKK creates criminal opportunities by “legitimising” itself across diasporas by invoking ideological sympathy and social dependence (conceptualised as “constructed legitimisers”), ensuring minimal resistance to its activities. SCP+N is motivated as an effective counterstrategy, addressing both the rational and impulsive nature of offending. The overall theoretical contribution of this paper is to assess overseas terrorist financing through a prevention-oriented, situational and behavioural framework, and to propose a community-based strategy to effectively counter such activities.

Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps

Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that up to now is only partially addressed. We show how to prove sharp polynomial bounds on decay of correlations for a class of multidimensional intermittent maps. In addition we show that the optimal results on statistical limit laws for one-dimensional intermittent maps hold also for the maps considered here. This includes the (functional) central limit theorem and local limit theorem, Berry-Esseen estimates, large deviation estimates, convergence to stable laws and Lévy processes, and infinite measure mixing.

Limit laws for the norms of extremal samples

Denote Sn(p)=kn−1∑i=1knlog(Xn+1−i,n∕Xn−kn,n)p, where p>0, kn≤n is a sequence of integers such that kn→∞ and kn∕n→0, and X1,n≤⋯≤Xn,n are the order statistics of iid random variables X1,…,Xn with regularly varying upper tail of index 1∕γ. The estimator γ̂(n)=(Sn(p)∕Γ(p+1))1∕p is an extension of the Hill estimator. We investigate the asymptotic properties of Sn(p) and γ̂(n) both for fixed p>0 and for p=pn→∞. We prove consistency for γ̂(n) and limit theorem for γ̂(n)−γ under appropriate assumptions. We obtain both Gaussian and non-Gaussian (stable) limit depending on the growth rate of the power sequence pn. Applied to real data we find that for larger p the estimator is less sensitive to the change in kn than the Hill estimator.

An Update on Postoperative Opioid Use and Alternative Pain Control Following Spine Surgery.

Opioids are commonly prescribed postoperatively for pain control, especially in spine surgery. Not only does this pose concerns for potential abuse, but it also has been shown to worsen certain outcomes. Risk factors for increased use include preoperative opioid use, female sex, psychiatric diagnoses, and drug and alcohol use. Over the past few decades, there have been increasing efforts mostly spearheaded by governmental agencies to decrease postoperative opioid use via opioid prescription limitation laws regulating the number of days and amounts of analgesics prescribed and promotion of the use of enhanced recovery after surgery (ERAS) protocols, multimodal pain regimens, epidural catheters, and ultrasound-guided peripheral nerve blocks. These strategies collectively have been efficacious in decreasing overall opioid use and better controlling patients' postoperative pain while simultaneously improving other outcomes such as postoperative nausea, vomiting, and length of stay. With an aging population undergoing an increasing number of spinal surgeries each year, it is now more important than ever to continue these efforts to improve the quality and safety of pain control methods after spinal surgery and limit the transition of acute management to the development of opioid dependence and addiction long-term.

Article 3(5) TEU a decade on: Revisiting ‘strict observance of international law’ in the text and context of other EU values

Article 3(5) of the Treaty on the European Union concerns EU external relations and was a new provision of the Lisbon Treaty. It has been seized upon by scholars for its reference to ‘strict observance of international law’ by the EU in its relations with the wider world. However, recent case law in the Court of Justice of the European Union has demonstrated little movement towards this supposed ideal. This article supports the fact that rigid and unquestioning adherence to international law has not emerged in case law, particularly as Article 3(5) TEU also mandates that the Union ‘uphold and promote its values and interests’. By taking a broader view of both the text and context of Article 3(5) TEU in EU law as a whole, and through consideration of the limited demands international law places on domestic courts, the article argues that – contrary to current literature – a more expressly balanced approach towards respect for international law is required and should be nurtured in the case law.

Random additions in urns of integers

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

Designs in Finite Metric Spaces: A Probabilistic Approach

A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that generalizes that of designs in Q-polynomial distance-regular graphs. An approximation of their cumulative distribution function, based on the notion of Christoffel function in approximation theory is given. As an application we derive limit laws on the weight distributions of binary orthogonal arrays of strength going to infinity. An analogous result for combinatorial designs of strength going to infinity is given.

The Class Action in Lithuania and Poland: History, Experiences and Lessons

Abstract The article analyses the peculiarities of the regulation of Class Action institution in the civil proceedings of Lithuania and Poland. Due to its limited scope, this article investigates the civil proceedings in the first instance courts only. The authors draw a special focus on the comparative analysis and the analysis of the effectiveness of the procedure in the current regulation by investigating both the doctrine and the available limited case law. The subject of considerations are problems relating both to the admissibility of filing a class action, as well as the course of court proceedings in cases concerning group proceedings, with particular emphasis on their differences from other procedural structures in Poland and Lithuania.

On the probability that a random subtree is spanning

AbstractWe consider the quantity associated with a graph that is defined as the probability that a randomly chosen subtree of is spanning. Motivated by conjectures due to Chin, Gordon, MacPhee and Vincent on the behaviour of this graph invariant depending on the edge density, we establish first that is bounded below by a positive constant provided that the minimum degree is bounded below by a linear function in the number of vertices. Thereafter, the focus is shifted to the classical Erdős–Rényi random graph model . It is shown that converges in probability to if and to 0 if . As side results, we find in the dense case that the total number of subtrees satisfies a log‐normal limit law, and that the number of vertices missing in a random subtree asymptotically follows a Poisson distribution.

Limit law for the cover time of a random walk on a binary tree

Let Tn denote the binary tree of depth n augmented by an extra edge connected to its root. Let Cn denote the cover time of Tn by simple random walk. We prove that the sequence of random variables Cn 2−(n+1)−mn, where mn is an explicit constant, converges in distribution as n→∞, and identify the limit.

Traffic Speed Rule Violation Detection System

Research has shown that the highest rates of road accident are caused by high-speed vehicles. In an attempt to mitigate this problem, the authority has specified speed limits on the roads in order to regulate the speed of vehicles. To successfully enforce the speed limit law, a mechanism for monitoring a vehicle speed is required. There are numerous measures in use for detecting and monitoring the speed limit violators. Some of these methods include the use of speed cameras, radar, loop detector, police officers, and many more. These traditional methods are not effective due to their setbacks, which ranges from the cost of acquiring equipment, increase labor and manpower, and inadequacy of monitoring. As such, a simple, cost effective and easily deployed speed detection technique that can overcome the shortcomings of the traditional methods imperative. In this paper, we proposed an automatic speed violation detection. The proposed system is cost effective and user centered.