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Consider a Cayley graph of some big finite group. Consider random walk on such a graph - think of it as drunk driver. Fix some number $N$ which is much smaller than group size. Question 1: How to ...

Let $G$ be a finite group, and let $Q$ be a probability measure on $G$. Suppose that $Q$, as a function on $G$, is supported on a conjugacy class $C$. We denote by $Q^{*k}$ the $k$-fold convolution of ...