A note on multi-type cookie random walk on integers
arXiv:0803.1664
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.
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)