The drift of a one-dimensional self-avoiding random walk
type: Item
instance of: scholarly article
title: The drift of a one-dimensional self-avoiding random walk
zbMATH Open document ID: 0792.60097
DOI: 10.1007/BF01200208
publication date: 1994-05-18T00:00:00Z
review text: We prove that a self-avoiding random walk on the integers with bounded increments grows linearly. We characterize its drift in terms of the Frobenius eigenvalue of a certain one-parameter family of primitive matrices. As an important tool, we express the local times as a two-block functional of a certain Markov chain, which is of independent interest.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 568995
zbMATH Keywords: self-avoiding random walk
zbMATH Keywords: local times
zbMATH Keywords: Markov chain
author: W. König
reviewed by: W. König
MaRDI profile type: Publication
cites work: Self-intersections of 1-dimensional random walks
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cites work: Q4692653
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cites work: A variational characterization of the speed of a one-dimensional self- repellent random walk
cites work: The drift of a one-dimensional self-repellent random walk with bounded increments
cites work: Non-negative matrices and Markov chains. 2nd ed
cites work: Asymptotic probabilities and differential equations
full work available at URL: https://doi.org/10.1007/bf01200208
OpenAlex ID: W2040171393
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568995