Related papers: The central limit theorem on nilpotent Lie groups

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…

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…

We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erd\H{o}s-R\'enyi graph. Special attention is given to the influence of initial condition (not…

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way.…

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…

We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on $\mathbb{Z}$ with unbounded memory which exhibits a phase transition from diffusive to superdiffusive behaviour. We prove a law of large…

We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…

We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson…

A famous result in renewal theory is the Central Limit Theorem for renewal processes. As in applications usually only observations from a finite time interval are available, a bound on the Kolmogorov distance to the normal distribution is…

We prove the existence of a limiting distribution for the appropriately rescaled diameters of random undirected Cayley graphs of finite nilpotent groups of bounded rank and nilpotency class, thus extending a result of Shapira and Zuck which…

Let $G$ be a group with a non-elementary action on a proper CAT(0) space $X$, and let $\mu$ be a measure on $G$ such that the random walk $(Z_n)_n$ generated by $\mu$ has finite second moment on $X$. Let $o$ be a basepoint in $X$, and…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

We show a central limit theorem for random walk on a Galton-Watson tree, when the edges of the tree are assigned randomly uniformly elliptic conductances. When a positive fraction of edges is assigned a small conductance $\varepsilon$, we…

We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus…

In statistics on manifolds, the notion of the mean of a probability distribution becomes more involved than in a linear space. Several location statistics have been proposed, which reduce to the ordinary mean in Euclidean space. A…

Given a Gromov-hyperbolic group $G$ endowed with a finite symmetric generating set, we study the statistics of counting measures on the spheres of the associated Cayley graph under linear representations of $G$. More generally, we obtain a…

We investigate random walks on the general linear group constrained within a specific domain, with a focus on their asymptotic behavior. In a previous work [38], we constructed the associated harmonic measure, a key element in formulating…

We consider a class of random billiards in a tube, where reflection angles at collisions with the boundary of the tube are random variables rather than deterministic (and elastic) quantities. We obtain a (non-standard) Central Limit Theorem…

We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…

Concentration inequalities, which have proved very useful in a variety of fields, provide fairly tight bounds on large deviation probabilities while central limit theorem (CLT) describes the asymptotic distribution around the mean (at the…