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.
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)