VRRW on complete-like graphs: almost sure behavior
type: Item
instance of: scholarly article
title: VRRW on complete-like graphs: almost sure behavior
zbMATH Open document ID: 1229.60057
DOI: 10.1214/10-AAP687
author: Vlada Limic
author: Stanislav Volkov
published in: The Annals of Applied Probability
publication date: 2010-12-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/0904.4722
review text: The authors study the vertex-reinforced random walk (VRRW) on complete-like graphs, i.e., complete graphs ornamented with finitely many leaves at each vertex. They combine martingale and large deviation techniques to prove that almost surely such VRRW spends positive and equal proportions of time on each of its nonleaf vertices. Previously [\textit{S. Volkov}, Ann. Probab. 29, No.~1, 66--91 (2001; Zbl 1031.60089)], it was shown that this behavior occurs only up to an event of positive probability. The convergence rate of the empirical occupation measure is studied as well.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 5829443
zbMATH Keywords: vertex-reinforced random walks
zbMATH Keywords: complete graph
zbMATH Keywords: urn model
zbMATH Keywords: martingales
zbMATH Keywords: large deviations
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
arXiv ID: 0904.4722
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OpenAlex ID: W3098553937
description: scientific article