Related papers: Central limit theorems for non-symmetric random wa…

We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the Central…

In this article we consider a natural class of random walks on free products of graphs, which arise as convex combinations of random walks on the single factors. From the works of Gilch [6,7] it is well-known that for these random walks the…

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…

Let $\Cal S$ be an abelian group of automorphisms of a probability space $(X, {\Cal A}, \mu)$ with a finite system of generators $(A_1, ..., A_d)$. Let $A^{\el}$ denote $A_1^{\ell_1} ... A_d^{\ell_d}$, for ${\el}= (\ell_1, ..., \ell_d)$. If…

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…

In 2010, Shiffman and Zelditch proved a central limit theorem (CLT) for smooth statistics of Gaussian random zeros in codimension one over compact K\"ahler manifolds. They raised the question of whether this result admits a two-fold…

The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…

We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our…

We study random walks on groups with the feature that, roughly speaking, successive positions of the walk tend to be "aligned". We formalize and quantify this property by means of the notion of deviation inequalities. We show that deviation…

We reduce the local limit theorem for a non-compact semisimple Lie group acting on its symmetric space to establishing that a natural operator associated to the measure is quasicompact. Under strong Diophantine assumptions on the underlying…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to…

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…

Consider a simple random walk on a realization of an Erd\H{o}s-R\'enyi graph. Assume that it is asymptotically almost surely (a.a.s.) connected. Conditional on an eigenvector delocalization conjecture, we prove a Central Limit Theorem (CLT)…

Let ${\cal T}$ be a rooted Galton-Watson tree with offspring distribution $\{p_k\}$ that has $p_0=0$, mean $m=\sum kp_k>1$ and exponential tails. Consider the $\lambda$-biased random walk $\{X_n\}_{n\geq 0}$ on ${\cal T}$; this is the…

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…

In this paper, we introduce a joint central limit theorem (CLT) for specific bilinear forms, encompassing the resolvent of the sample covariance matrix under an elliptical distribution. Through an exhaustive exploration of our theoretical…

We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We…

We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's…

We prove a central limit theorem for random walks with finite variance on linear groups.