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

Abstract

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 $\omega (x)\in [\frac{1}{2},1)$, 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 $\frac{1}{2}$. 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.

This version adds a monotonicity result which was missing from the previous version

References in corpus (1)

• Excited Random Walk