Isoperimetric profiles and random walks on some groups defined by piecewise actions

2020/08/28 by Laurent Saloff-Coste-Costeb, Tianyi Zheng, Saloff-Coste-Costeb, Laurent +1
Mathematics · #20B35 #60B15 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2008.12872

openalex publication_date 2020/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple \em gluing of such. In one of our simplest constructions---the \em pocket-extension of a group G---this leads to the study of certain finitely generated subgroups of the full permutation group \mathbb S(G∪ \*\). Some sharp estimates are obtained while many challenging questions remain.

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