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Let $\{X_t\}_{t=-\infty}^{\infty}$ be a sequence of random variables. We are interested in a "random walk" (or more generally, a random field) that can be characterized by $$ X_t ~|~ X_{t-k}, \ldots, ...

Let $\Gamma$ denote the Cayley graph for a finitely generated group $G$, and let $p_n(x, y)$ denote the transition probability that a random walk starting at $x$ reaches $y$ at time $n$. A famous &...

In Diaconis's book Group Representations in Probability and Statistics, Chapter 3C, there are explicit computations for the mixing time of the random walk on the cycle graph $\mathbb{Z}_{p}$, with $p$ ...