---
abstract: 'We introduce a generalization of expander graphs, which is called a weak expander sequence. It is proved that a uniform Roe algebra of a weak expander sequence is not locally reflexive. It follows that uniform Roe algebras of expander graphs are not exact. We introduce the notion of a generalized box space to discuss box spaces and expander sequences in a unified framework. Key tools for the proof are amenable traces and measured groupoids associated with generalized box spaces.'
address: 'Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan'
author:
- Hiroki Sako
bibliography:
- 'wexpander.bib'
title: A generalization of expander graphs and local reflexivity of uniform Roe algebras
---

Introduction
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An expander sequence is a family of finite graphs which are uniformly locally finite but highly connected. It has applications to computer sciences, error correcting codes, and networks. The first explicit example of an expander sequence was constructed by Margulis [@MargulisExpander]. It was constructed from a residually finite group with relative property (T).

Expander graphs give important examples in coarse geometry. Coarse geometry is a study of ‘large scale uniform structure’ of a space. We study features which do not depend on the local structure. 