Vertex-reinfoced random walk on Z visits finitely many states
Probability
2016-09-07 v1
Abstract
Vertex-reinforced random walk is defined in Pemantle's (1988) thesis; it is a random walk that is biased to visit sites it has already visited a lot. We show that this reinforcement scheme, in contrast to the scheme of edge-reinforcement, causes random walk on a line to get trapped in a finite set.
Cite
@article{arxiv.math/9701224,
title = {Vertex-reinfoced random walk on Z visits finitely many states},
author = {Robin Pemantle and Stanislav Volkov},
journal= {arXiv preprint arXiv:math/9701224},
year = {2016}
}