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A bound on the square distance of a random walk on undirected graph
Fact:
Let $G$ be an $n$-vertex undirected graph and $(X_s)_{s\in \mathbb N}$ a stationary random walk on $G$. Then for every $s\in \mathbb{N}$,
$ \mathbb{E}[d_G(X_s,X_0)^2] \le C s \log n $, for some ...
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