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

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

2009-02-06

arxiv.org/abs/0902.1026v3

Mathematics

Probability

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

Scientific paper

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.

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