Revista Matemática Iberoamericana


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Volume 29, Issue 2, 2013, pp. 715–737
DOI: 10.4171/RMI/736

Published online: 2013-04-22

Isoperimetric profile and random walks on locally compact solvable groups

Romain Tessera[1]

(1) Université Paris-Sud, Orsay, France

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.

Keywords: Solvable locally compact groups, isoperimetric profile, random walks on groups, $L^p$-cohomology, uniform embeddings into Banach spaces

Tessera Romain: Isoperimetric profile and random walks on locally compact solvable groups. Rev. Mat. Iberoamericana 29 (2013), 715-737. doi: 10.4171/RMI/736