Phase transition for the Once-reinforced random walk on Z^sup d^-like trees

Phase transition for the Once-reinforced random walk on Z^sup d^-like trees

In this short paper, we consider the Once-reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit critical parameter a0 such that the Once-reinforced random walk...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of probability Vol. 46; no. 4; p. 2121
Main Authors: Kious, Daniel, Sidoravicius, Vladas
Format: Journal Article
Language:English
Published: Hayward Institute of Mathematical Statistics 01-07-2018
Subjects:
Decision trees
Parameters
Phase transitions
Random walk
Random walk theory
Studies
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this short paper, we consider the Once-reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit critical parameter a0 such that the Once-reinforced random walk is almost surely recurrent if a>a0 and almost surely transient if a<a0. This provides the first examples of phase transition for the Once-reinforced random walk.
ISSN:0091-1798
2168-894X