# Transience/Recurrence and the speed of a one-dimensional random walk in a "have your cookie and eat it" environment

Authors
Type
Preprint
Publication Date
Jun 07, 2009
Submission Date
Feb 06, 2009
Identifiers
DOI: 10.1214/09-AIHP331
Source
arXiv
Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $\omega(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$, from which time onward the probability of jumping to the right is $\frac12$. We investigate the transience/recurrence properties of this process in both deterministic and stationary, ergodic environments $\{\omega(x)\}_{x\in Z}$. In deterministic environments, we also study the speed of the process.