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Speed of random walks

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How fast does a random walk on a graph escape from its starting point? In this survey talk, I will consider this question in a variety of settings:

Simple RW on Galton-Watson trees, where speed can be computed

RW on lamplighter groups: The Kaimanovich-Vershik Theorem

Which escape exponents are possible for RW on groups?

Benjamini-Lyons-Schramm conjecture: percolation preserves speed of RW

The effect of bias for RW on trees and on groups

Surprisingly, the expected distance from the starting point can be non-monotone, even when starting at the stationary distribution and the walk has holding probability 1/2.

*The square root lower bound on groups: Can it be proved beyond the inverse spectral gap?

This talk is part of the Probability series.

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