Phase transition in vertex-reinforced random walks on Z with non-linear reinforecment

S Volkov

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)

Abstract

Vertex-reinforced random walk is a random process which visits a site with probability proportional to the weight w_k of the number k of previous visits. We show that if w_k∼k^α, then there is a large time T such that after T the walk visits 2, 5, or ∞ sites when α1, respectively. More general results are also proven.
Translated title of the contributionPhase transition in vertex-reinforced random walks on Z with non-linear reinforecment
Original languageEnglish
Pages (from-to)691 - 700
Number of pages10
JournalJournal of Theoretical Probability
Volume19
Publication statusPublished - Dec 2006

Bibliographical note

Publisher: Springer

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