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We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that…

Probability · Mathematics 2025-09-12 Gabriel Raposo

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…

Dynamical Systems · Mathematics 2023-07-25 Yeor Hafouta

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting It\^o-type diffusion…

Probability · Mathematics 2021-10-19 Le Chen , Davar Khoshnevisan , David Nualart , Fei Pu

We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of "homogenization" for Dyson Brownian Motion, this yields the universality of quantities which depend on…

Probability · Mathematics 2019-11-28 Benjamin Landon , Philippe Sosoe

The aim of this paper is to prove the strong law of large numbers (SLLN) as well as the central limit theorem (CLT) for a class of vector-valued stochastic processes which arise as solutions of the stochastic evolution inclusion…

Probability · Mathematics 2018-02-27 Alexander Nerlich

We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing with the size of the matrix. In particular,…

Probability · Mathematics 2026-04-30 Indrajit Jana , Sunita Rani

In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie…

Dynamical Systems · Mathematics 2017-06-29 Michael Björklund , Alexander Gorodnik

Fr\'echet means of samples from a probability measure $\mu$ on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). The methods and results proceed by introducing and…

Probability · Mathematics 2023-11-17 Jonathan C. Mattingly , Ezra Miller , Do Tran

There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…

Probability · Mathematics 2020-10-15 Daniel Remenik

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the…

Probability · Mathematics 2012-03-02 Alexander Bulinski , Evgeny Spodarev , Florian Timmermann

In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…

Probability · Mathematics 2024-03-27 Jürgen Angst , Ronan Herry , Dominique Malicet , Guillaume Poly

We discuss the spectral asymptotics of some open subsets of the real line with random fractal boundary and of a random fractal, the continuum random tree. In the case of open subsets with random fractal boundary we establish the existence…

Probability · Mathematics 2016-12-08 Philippe H. A. Charmoy , David A. Croydon , Ben M. Hambly

It is well-known that, on a purely algebraic level, a simplified algebraic version of the Central Limit Theorem (CLT) can be proved in the framework of a noncommutative probability space, under the hypotheses that the sequence of…

Probability · Mathematics 2022-12-13 Claus Koestler , Alexandru Nica

We establish a central limit theorem for the fluctuations of the linear statistics in the $\beta$-ensemble of dimension $N$ at a temperature proportional to $N$ and with confining smooth potential. In this regime, the particles do not…

Probability · Mathematics 2024-11-12 Charlie Dworaczek Guera , Ronan Memin

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

Probability · Mathematics 2010-02-08 Ivan Nourdin , Giovanni Peccati

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…

Probability · Mathematics 2012-09-25 Christian Döbler , Michael Stolz

Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…

Statistics Theory · Mathematics 2009-09-29 Yuliya V. Martsynyuk

We prove, for any $\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at…

Probability · Mathematics 2018-09-11 Thomas Leblé

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time…

Quantum Physics · Physics 2018-05-28 Mohammad Mehboudi , Anna Sanpera , Juan M. R. Parrondo

We study the fluctuations of a stochastic epidemic model with memory of the last infections, varying infectivity, and waning immunity, as introduced in Guerin and Zotsa-Ngoufack:arXiv preprint arXiv:2505.00601. The dynamics of the epidemic…

Probability · Mathematics 2025-05-28 Arsene Brice Zotsa-Ngoufack