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We consider the totally asymmetric simple exclusion process on $\Z$ with step initial condition and with the presence of a rightward-moving wall that prevents the particles from jumping. This model was first studied in…

Probability · Mathematics 2025-09-03 Patrik L. Ferrari , Sabrina Gernholt

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…

Dynamical Systems · Mathematics 2017-11-06 Jacopo De Simoi , Carlangelo Liverani

We prove moderate deviation principles for the tagged particle position and current in one-dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate $1/2$,…

Probability · Mathematics 2022-03-11 Xiaofeng Xue , Linjie Zhao

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution…

Mathematical Physics · Physics 2007-08-18 T. Imamura , T. Sasamoto

In this paper, we consider U-statistics whose data is a strictly stationary sequence which can be expressed as a functional of an i.i.d. one. We establish a strong law of large numbers, a bounded law of the iterated logarithms and a central…

Probability · Mathematics 2021-04-22 Davide Giraudo

We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…

Probability · Mathematics 2024-11-13 Patrick van Meurs , Kenkichi Tsunoda , Lu Xu

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

Combinatorics · Mathematics 2024-09-25 Aaron Abrams , Eric Babson , Henry Landau , Zeph Landau , James Pommersheim

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…

Probability · Mathematics 2018-04-10 Khanh Duy Trinh

In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…

Probability · Mathematics 2021-12-07 Benjamin Jourdain , Alvin Tse

The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…

Dynamical Systems · Mathematics 2020-12-02 Davor Dragičević , Yeor Hafouta

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

Probability · Mathematics 2025-01-29 Alexander Shmyrov , Vasily Shmyrov

The de Moivre-Laplace theorem is a special case of the central limit theorem for Bernoulli random variables, and can be proved by direct computation. We deduce the central limit theorem for any random variable with finite variance from the…

Probability · Mathematics 2021-10-29 Calvin Wooyoung Chin

We investigate the tagged-particle motion in a strongly interacting quasi-confined liquid using periodic boundary conditions along the confining direction. Within a mode-coupling theory of the glass transition (MCT) we calculate the…

Soft Condensed Matter · Physics 2021-09-14 Lukas Schrack , Charlotte F. Petersen , Michele Caraglio , Gerhard Jung , Thomas Franosch

Under natural assumptions on the observable, we prove a Central Limit Theorem, a Berry-Esseen Theorem, and a quantitative Local Limit Theorem for a broad class of partially hyperbolic endomorphisms of the two-dimensional torus. Our results…

Dynamical Systems · Mathematics 2025-07-21 Roberto Castorrini , Kasun Fernando

In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…

Probability · Mathematics 2022-02-11 Michael Fleermann , Werner Kirsch

We study the equilibrium fluctuations of a tagged particle in finite-range simple exclusion processes on Z^d with biased single particle jump rates. It is known the variance of the tagged particle at time t is diffusive, that is on order…

Probability · Mathematics 2007-05-23 Sunder Sethuraman

Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common…

Methodology · Statistics 2022-09-20 Jinyong Hahn , Guido Kuersteiner , Maurizio Mazzocco

We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results…

Statistical Mechanics · Physics 2015-10-19 Gunter M. Schütz

We prove a criteria for uniform hyperbolicity based on the periodic points of the transformation. More precisely, if a mild (non uniform) hyperbolicity condition holds for the periodic points of any diffeomorphism in a residual subset of a…

Dynamical Systems · Mathematics 2012-06-13 Armando Castro

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…

Probability · Mathematics 2012-10-02 Olivier Durieu , Marco Tusche