Related papers: Random walks in Weyl chambers and crystals

The paper deals with renewal theory for a class of extremal Markov sequences connected with the Kendall convolution. We consider here some particular cases of the Wold processes associated with generalized convolutions. We prove an analogue…

Let $\mm_n, n=0,1,...$ be the supercritical branching random walk, in which the number of direct descendants of one individual may be infinite with positive probability. Assume that the standard martingale $W_n$ related to $\mm_n$ is…

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…

In this paper we consider the argmin process of random walks and L\'evy processes. We prove that they enjoy the Markov property, and provide their transition kernels in some special cases.

We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…

We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…

As a model of trapping by biased motion in random structure, we study the time taken for a biased random walk to return to the root of a subcritical Galton-Watson tree. We do so for trees in which these biases are randomly chosen,…

We study an irreducible Markov chain on the category of finite abelian $p$-groups, whose stationary measure is the Cohen-Lenstra distribution. This Markov chain arises when one studies the cokernel of a random matrix $M$, after conditioning…

The main aim of the present set of notes is to give new, short and essentially self-contained proofs of some classical, as well as more recent, results about random walks on groups. For instance, we shall see that the drift characterization…

We continue the line of research of random walks with barrier initiated by Iksanov and M{\"o}hle (2008). Assuming that the tail of the step of the underlying random walk has a power-like behavior at infinity with exponent $-\alpha$,…

We study lattice walks in a Weyl chamber of type A with fixed or free end points. For lattice walk models with zero drift that may be counted by means of a reflection argument, we determine asymptotics for the number of such walks as their…

This is a preprint of Chapter 2 in the following work: Marta Lewicka, A Course on Tug-of-War Games with Random Noise, 2020, Springer, reproduced with permission of Springer Nature Switzerland AG. We present the basic relation between the…

We consider a discrete-time random motion, Markov chain on the Poincar\'{e} disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its location is determined by a composition of random…

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the…

We study random walks in a random environment on a regular, rooted, coloured tree. The asymptotic behaviour of the walks is classified for ergodicity/transience in terms of the geometric properties of the matrix describing the random…

We study a random walk on a complex of finitely many half-lines joined at a common origin; jumps are heavy-tailed and of two types, either one-sided (towards the origin) or two-sided (symmetric). Transmission between half-lines via the…

We study recurrence properties and the validity of the (weak) law of large numbers for (discrete time) processes which, in the simplest case, are obtained from simple symmetric random walk on $\Z$ by modifying the distribution of a step…

The paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on $\mathbb{Z}$. This result appears as an extension of the invariance principal theorem for classical random walks on $\mathbb{Z}$ or…