Phase transition in vertex-reinforced random walks on Z with non-linear reinforcement
(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:
https://lup.lub.lu.se/record/4588127
- author
- Volkov, Stanislav LU
- publishing date
- 2006
- 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
- 2022-04-20 22:19:47
@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 < 1, = 1, or > 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}}, }