Volume growth, random walks and electric resistance in vertex-transitive graphs

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• Matthew Tointon (University of Cambridge)
• Wednesday 13 November 2019, 13:45-14:45
• MR5, CMS.

If you have a question about this talk, please contact Thomas Bloom.

An infinite connected graph G is called recurrent if, with probability 1, the simple random walk on G it eventually returns to its starting point. Varopoulos famously showed that a Cayley graph has a recurrent random walk if and only if the underlying group has a finite-index subgroup isomorphic to Z or Z^2. A key step is to show that a recurrent Cayley graph has at most quadratic volume growth – that is, the cardinality of the ball of radius n about the identity grows at most quadratically in n. In this talk I will describe some finitary versions of these statements. In particular, I will present an analogue of Varopoulos’s theorem for finite Cayley graphs, resolving a conjecture of Benjamini and Kozma. This is joint work with Romain Tessera.

This talk is part of the Discrete Analysis Seminar series.

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