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

Volkov, Stanislav LU orcid (2006) In Journal of Theoretical Probability 19(3). p.691-700
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 0 such that after T 0 the walk visits 2, 5, or ∞ sites when α < 1, = 1, or > 1, respectively. More general results are also proven.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Vertex-reinforced random walks urn models Rubin’s construction
in
Journal of Theoretical Probability
volume
19
issue
3
pages
691 - 700
publisher
Springer
external identifiers
  • scopus:33845660295
ISSN
1572-9230
DOI
10.1007/s10959-006-0033-2
language
English
LU publication?
no
id
537c4fa3-cad5-41b7-8e43-568c16b081d9 (old id 4588127)
date added to LUP
2016-04-01 11:49:10
date last changed
2025-10-14 10:26:37
@article{537c4fa3-cad5-41b7-8e43-568c16b081d9,
  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 0 such that after T 0 the walk visits 2, 5, or ∞ sites when α &lt; 1, = 1, or &gt; 1, respectively. More general results are also proven.}},
  author       = {{Volkov, Stanislav}},
  issn         = {{1572-9230}},
  keywords     = {{Vertex-reinforced random walks urn models Rubin’s construction}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{691--700}},
  publisher    = {{Springer}},
  series       = {{Journal of Theoretical Probability}},
  title        = {{Phase transition in vertex-reinforced random walks on Z with non-linear reinforcement}},
  url          = {{https://lup.lub.lu.se/search/files/2655819/4588730.pdf}},
  doi          = {{10.1007/s10959-006-0033-2}},
  volume       = {{19}},
  year         = {{2006}},
}