On sofic approximations of Property (T) groups

Abstract

We prove Bowen's conjecture that every sequence of finite graphs that locally converges to the Cayley graph of a countably infinite group with Kazhdan Property (T) is essentially a vertex-disjoint union of expander graphs. We characterize graph sequences that are essentially a vertex-disjoint union of expander graphs in terms of the Markov operator.

The use of different notions of expanders has been confusing in the earlier versions, where one-sided and two-sided expanders have not been distinguished (Theorem 2 in v1-v3) sufficiently. Theorem 3 and Corollary 5 deal with these separately

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