English

A note on multi-type cookie random walk on integers

Probability 2008-12-18 v2

Abstract

We consider a random walk on integers where at the first visits to a site the walker gets a positive drift, but where after a certain number of visits the walker gets a negative drift. We prove that the walker is almost surely transient to the left with positive speed.

Keywords

Cite

@article{arxiv.0803.1664,
  title  = {A note on multi-type cookie random walk on integers},
  author = {Bruno Schapira},
  journal= {arXiv preprint arXiv:0803.1664},
  year   = {2008}
}

Comments

As noticed by a referee, the result of this note follows from a recent result of Kosygina and Zerner (simply by using a monotonicity argument)

R2 v1 2026-06-21T10:20:40.505Z