On measured expanders

Abstract: By a "measured graph" we simply mean a graph with weights assigned to its vertices. The classical isoperimetric (a.k.a. Cheeger) constant describing connectedness of a graph generalises to this setting, leading to a notion of a "measured expander": a sequence of finite graphs with a uniform positive lower bound on this isoperimetric constant. The talk will walk through a bit of coarse geometry to a functional analytic question that led us to consider this notion. Our main result is a characterisation of measured expanders through a Poincare inequality, and thus that they do not coarsely embed into $L^p$-space. I will also present some examples. Based on joint work with K. Li and J. Zhang.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.