Random Walks in Dirichlet Random Environments on $\mathbb{Z}$ with Bounded Jumps

Autor:	Slonim, Daniel J.
Rok vydání:	2021
Předmět:	Mathematics - Probability 60G50 60J10 60K37
Druh dokumentu:	Working Paper
Popis:	We examine a class of random walks in random environments on $\mathbb{Z}$ with bounded jumps, a generalization of the classic one-dimensional model. The environments we study have i.i.d. transition probability vectors drawn from Dirichlet distributions. For this model, we characterize recurrence and transience, and in the transient case we characterize ballisticity. For ballisticity, we give two parameters, $\kappa_0$ and $\kappa_1$. The parameter $\kappa_0$ governs finite trapping effects, and $\kappa_1$ governs repeated traversals of arbitrarily large regions of the graph. We show that the walk is right-transient if and only if $\kappa_1>0$, and in that case it is ballistic if and only if $\min(\kappa_0,\kappa_1)>1$. Comment: 60 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.14950 Zobrazit plný text záznamu View this record from Arxiv