# Speed of the biased random walk on a Galton-Watson tree

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When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and that a sharp cutoff phenomenon...

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Veraverbeke's (Stoch Proc Appl 5:27-37, ) theorem relates the tail of the distribution of the supremum of a random walk with negative drift to the tail of the distribution of its increments, or equivalently, the probability that a centered random walk with heavy-tail increments hits a moving...