A zero-one law for planar random walks in random environment
type: Item
instance of: scholarly article
title: A zero-one law for planar random walks in random environment
zbMATH Open document ID: 1016.60093
author: Franz Merkl
author: Martin P. W. Zerner
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: The main purpose of the paper is the derivation of a zero-one law for random walks \((X_n)_n\) in i.i.d. random environment on \(Z^2\). It is shown that for any fixed direction \(l\in R^2\setminus \{0\}\) the event that the inner product \(X_nl\) tends to \(+\infty\) as \(n\to \infty\) has probability either 0 or 1. This is a solution of the problem posed by S. A. Kalikow whether the event that the \(x\)-coordinate of a random walk in a two-dimensional random environment approaches \(\infty\) has necessarily probability either zero or one.
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 82B41
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 60F20
zbMATH DE Number: 1906037
zbMATH Keywords: random walk in random environment
zbMATH Keywords: zero-one law
reviewed by: U. A. Rozikov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1015345769
OpenAlex ID: W1512856531
cites work: Shift-coupling and a zero-one law for random walk in random environment
cites work: Generalized random walk in a random environment
cites work: Reflection and coalescence between independent one-dimensional Brownian paths
cites work: A law of large numbers for random walks in random environment
DOI: 10.1214/AOP/1015345769
description: scientific article; zbMATH DE number 1906037