Revista Matemática Iberoamericana
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Published online: 2013-04-22
Isoperimetric profile and random walks on locally compact solvable groupsRomain Tessera (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. Iberoam. 29 (2013), 715-737. doi: 10.4171/RMI/736