English

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.

Keywords

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}
}