Essential Expansion is Forceable

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• Gabor Kun (Rényi Institute)
• Wednesday 16 November 2016, 14:30-15:30
• MR5.

If you have a question about this talk, please contact Andrew Thomason.

We say that a sequence of bounded degree graphs is locally (Benjamini-Schramm) convergent if for every r the probability distribution on the isomorphism classes of rooted r-balls obtained by picking a vertex x uniformly at random and considering the r-ball centred at x converges in distribution. Not much is known about approximation of large graphs by small ones. We do not even know if every Cayley graph can be approximated by finite graphs: This is the famous problem if every group is sofic.

We prove Bowen’s conjecture that for every group G with Kazhdan Property (T) if a sequence of bounded degree graphs locally converges to a Cayley graph of G then the sequence is essentially a vertex-disjoint union of expander graphs. We characterize such sequences in terms of the Markov operator.

This talk is part of the Combinatorics Seminar series.

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