Isoperimetric profile and random walks on locally compact solvable groups

Romain Tessera

doi:10.4171/rmi/736

Isoperimetric profile and random walks on locally compact solvable groups

Romain Tessera

CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Research output: Contribution to journal › Article › peer-review

Abstract

We study the large-scale geometry of a large class of amenable locally compact groups comprising all solvable algebraic groups over a local field and their discrete subgroups. We show that the isoperimetric profile of these groups is in some sense optimal among amenable groups. We use this fact to compute the probability of return of symmetric random walks, and to derive various other geometric properties.

Original language	English
Pages (from-to)	715-737
Number of pages	23
Journal	Revista Matematica Iberoamericana
Volume	29
Issue number	2
DOIs	https://doi.org/10.4171/rmi/736
Publication status	Published - 1 Jan 2013
Externally published	Yes

Keywords

Isoperimetric profile
Lpcohomology
Random walks on groups
Solvable locally compact groups
Uniform embeddings into Banach spaces

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10.4171/rmi/736

Cite this

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KW - Lpcohomology

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KW - Uniform embeddings into Banach spaces

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Isoperimetric profile and random walks on locally compact solvable groups

Abstract

Keywords

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