On the range of reversible random walks on \(Z^ 2\) in a random environment
type: Item
instance of: scholarly article
title: On the range of reversible random walks on \(Z^ 2\) in a random environment
zbMATH Open document ID: 0819.60058
DOI: 10.1007/BF02212888
published in: Journal of Theoretical Probability
publication date: 1995-05-23T00:00:00Z
review text: Asymptotic behaviours of random walk in random environment rely on the independent increment property of the walk on \(Z^ d\), \(d \geq 1\). The paper discusses reversible random walks on \(Z^ d\), whose increments are not independent, and attempts to establish the law of large numbers for the range of these random walks. The main technical tools are hitting times and hitting distributions. The main result refers to the two- dimensional reversible random walk. The reversibility is here an assumption coming from the connection between the electrical network and the reversible random walk. The analysis cannot be extended to an irreversible random walk.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 757605
zbMATH Keywords: effective resistance
zbMATH Keywords: random walk
zbMATH Keywords: random environment
zbMATH Keywords: law of large numbers
zbMATH Keywords: irreversible random walk
author: Xian Yin Zhou
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02212888
OpenAlex ID: W1974121421
description: scientific article; zbMATH DE number 757605