Related papers: A Central Limit Theorem for Convolution Equations …

Let $\rho$ be a probability measure on $\mathrm{SL}\_d(\mathbb{Z})$ and consider the random walk defined by $\rho$ on the torus $\mathbb{T}^d = \mathbb{R}^d/\mathbb{Z}^d$. Bourgain, Furmann, Lindenstrauss and Mozes proved that under an…

The paper deals with a new class of random walks strictly connected with the Pareto distribution. We consider stochastic processes in the sense of generalized convolution or weak generalized convolution following the idea given in [1]. The…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…

We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of…

Certain renewal theorems are extended to the case that the rate of the renewal process goes to 0 and, more generally, to the case that the drift of the random walk goes to infinity. These extensions are motivated by and applied to the…

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…

We establish a quenched local central limit theorem for the dynamic random conductance model on $\mathbb{Z}^d$ only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show H\"older…

We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack…

We consider generalized inversions and descents in finite Weyl groups. We establish Coxeter-theoretic properties of indicator random variables of positive roots such as the covariance of two such indicator random variables. We then compute…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk repeats one of its preceding steps chosen uniformly at…

In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work of the first author, in which this information was obtained from forwards-in-time dynamics…

This work focuses on the temporal average of the backward Euler--Maruyama (BEM) method, which is used to approximate the ergodic limit of stochastic ordinary differential equations with super-linearly growing drift coefficients. We give the…

We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…

We consider a random walk on a supercritical Galton-Watson tree with leaves, where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree. The biases are chosen independently on…

We provide complementary results for a family of models with dependence on their previous $k$-sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass.…

Let $(W_n(\theta))_{n\in\mathbb N_0}$ be the Biggins martingale associated with a supercritical branching random walk and denote by $W_\infty(\theta)$ its limit. Assuming essentially that the martingale $(W_n(2\theta))_{n\in\mathbb N_0}$ is…

We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…