Co-spectral radius of intersections

2022/06/28 by Fraczyk, Mikolaj, van Limbeek, Wouter
#05C81 #20F69 #22D40 #22F10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.14251

Abstract

We study the behavior of the co-spectral radius of a subgroup H of a discrete group Γ under taking intersections. Our main result is that the co-spectral radius of an invariant random subgroup does not drop upon intersecting with a deterministic co-amenable subgroup. As an application, we find that the intersection of independent co-amenable invariant random subgroups is co-amenable.

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