Senile reinforced random walks

M. Holmes, A. Sakai

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider random walks with transition probabilities depending on the number of consecutive traversals nn of the edge most recently traversed. Such walks may get stuck on a single edge, or have every vertex recurrent or every vertex transient, depending on the reinforcement function f(n)f(n) that characterizes the model. We prove recurrence/transience results when the walk does not get stuck on a single edge. We also show that the diffusion constant need not be monotone in the reinforcement.
Original languageEnglish
Pages (from-to)1519-1539
Number of pages1
JournalStochastic Processes and their Applications
Volume117
Issue number10
DOIs
Publication statusPublished - Oct 2007

Fingerprint

Reinforced Random Walk
Reinforcement
Walk
Transience
Vertex of a graph
Transition Probability
Recurrence
Consecutive
Random walk
Monotone
Model

Cite this

Senile reinforced random walks. / Holmes, M.; Sakai, A.

In: Stochastic Processes and their Applications, Vol. 117, No. 10, 10.2007, p. 1519-1539.

Research output: Contribution to journalArticle

Holmes, M. ; Sakai, A. / Senile reinforced random walks. In: Stochastic Processes and their Applications. 2007 ; Vol. 117, No. 10. pp. 1519-1539.
@article{954ce683aa0f4e9cb24e24b6514e6f97,
title = "Senile reinforced random walks",
abstract = "We consider random walks with transition probabilities depending on the number of consecutive traversals nn of the edge most recently traversed. Such walks may get stuck on a single edge, or have every vertex recurrent or every vertex transient, depending on the reinforcement function f(n)f(n) that characterizes the model. We prove recurrence/transience results when the walk does not get stuck on a single edge. We also show that the diffusion constant need not be monotone in the reinforcement.",
author = "M. Holmes and A. Sakai",
year = "2007",
month = "10",
doi = "10.1016/j.spa.2007.02.003",
language = "English",
volume = "117",
pages = "1519--1539",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "10",

}

TY - JOUR

T1 - Senile reinforced random walks

AU - Holmes, M.

AU - Sakai, A.

PY - 2007/10

Y1 - 2007/10

N2 - We consider random walks with transition probabilities depending on the number of consecutive traversals nn of the edge most recently traversed. Such walks may get stuck on a single edge, or have every vertex recurrent or every vertex transient, depending on the reinforcement function f(n)f(n) that characterizes the model. We prove recurrence/transience results when the walk does not get stuck on a single edge. We also show that the diffusion constant need not be monotone in the reinforcement.

AB - We consider random walks with transition probabilities depending on the number of consecutive traversals nn of the edge most recently traversed. Such walks may get stuck on a single edge, or have every vertex recurrent or every vertex transient, depending on the reinforcement function f(n)f(n) that characterizes the model. We prove recurrence/transience results when the walk does not get stuck on a single edge. We also show that the diffusion constant need not be monotone in the reinforcement.

UR - http://dx.doi.org/10.1016/j.spa.2007.02.003

U2 - 10.1016/j.spa.2007.02.003

DO - 10.1016/j.spa.2007.02.003

M3 - Article

VL - 117

SP - 1519

EP - 1539

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 10

ER -