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Transience/recurrence and the speed of a one-dimensional random walk in a “have your cookie and eat it” environment

Ross G. Pinsky (2010)

Annales de l'I.H.P. Probabilités et statistiques

Consider a variant of the simple random walk on the integers, with the following transition mechanism. At each site x, the probability of jumping to the right is ω(x)∈[½, 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 ½. We investigate the transience/recurrence properties of this process in both deterministic and stationary, ergodic environments {ω(x)}x∈Z. In deterministic environments, we also study the speed...

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