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 GaltonWatson trees, where speed can be computed
RW on lamplighter groups: The KaimanovichVershik Theorem
Which escape exponents are possible for RW on groups?
BenjaminiLyonsSchramm 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
nonmonotone,
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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