Suppose that $G$ is a (locally finite) graph such that the simple random walk on $G$ is recurrent. Does this imply any upper bound on the speed $\mathbb{E}d(X_t,X_0)$ of such random walk?
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$\begingroup$ can you please define the speed precisely? $\endgroup$– Delio MugnoloCommented Nov 10, 2013 at 5:42
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$\begingroup$ @DelioM. : we start a random walk at point X_0 and look at the expected distance from X_0 after t steps (this might a priori depend on the choice of X_0). $\endgroup$– Marcin KotowskiCommented Nov 10, 2013 at 17:04
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$\begingroup$ i see. i don't know exactly what kind of estimates you are looking for, but you might find something relevant for you in §1.5 of fan chung's spectral graph theory or in chapter 1 of woess' random walks on infinite graphs and groups. $\endgroup$– Delio MugnoloCommented Nov 11, 2013 at 0:31
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