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Random walks on groups and the Kaimanovich-Vershik conjecture

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In the 1980s, much progress was made in understanding random walks on groups. In particular, characterizations of when there are non-constant bounded harmonic functions were given using asymptotic entropy. Later, Kaimanovich gave criteria for identifying all bounded harmonic functions. However, a conjecture of Kaimanovich and Vershik from 1979 remained open, with the first breakthrough by Erschler in 2011. We present a simple proof of the full conjecture in joint work with Yuval Peres.

This talk is part of the Probability series.

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