Conservative random walk*
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 th