Related papers: Non-homogeneous random walks with non-integrable i…

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the…

Infinite sums of i.i.d. random variables discounted by a multiplicative random walk are called perpetuities and have been studied by many authors. The present paper provides a log-type moment result for such random variables under minimal…

A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the…

We introduce a multidimensional walk with memory and random tendency. The asymptotic behaviour is characterized, proving a law of large numbers and showing a phase transition from diffusive to superdiffusive regimes. In first case, we…

This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic…

L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e.,…

Let $G$ be an infinite, locally finite graph. We investigate the relation between supercritical, transient branching random walk and the Martin boundary of its underlying random walk. We show results regarding the typical asymptotic…

We prove large-time $L^2$ and distributional limit theorems for perimeter and diameter of the convex hull of $N$ trajectories of planar random walks whose increments have finite second moments. Earlier work considered $N \in \{1,2\}$ and…

Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ having increments $(1,0)$, $(-1,1)$, $(0,-1)$ with jump probabilities $\lambda(M_k)$, $\mu_1(M_k)$, and $\mu_2(M_k)$ where $M$ is an irreducible aperiodic finite state Markov…

The aim of this paper is to deepen the analysis of the asymptotic behavior of the so-called minimal random walk (MRW) using a new martingale approach. The MRW is a discrete-time random walk with infinite memory that has three regimes…

We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…

We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…

This is the second in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. The first…

We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…

This paper explores the joint behaviour of the summands of a random walk when their mean value goes to infinity as its length increases. It is proved that all the summands must share the same value, which extends previous results in the…

For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infinite values) determined by the starting point x,…

We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…