Conservative random walk

Citeable URL: https://scholar.colorado.edu/concern/articles/12579t98j

Abstract

Recently, in [11], the “coin-turning walk” was introduced on Z. It is a non-Markovian process where the steps form a (possibly) time-inhomogeneous Markov chain. In this article, we follow up the investigation by introducing analogous processes in Zd, d ≥ 2: at time n the direction of the process is “updated” with probability pn; otherwise the next step repeats the previous one. We study some of the fundamental properties of these walks, such as transience/recurrence and scaling limits.

Our results complement previous ones in the literature about “correlated” (or “Newtonian”) and “persistent” random walks.

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