Isoperimetric profile and random walks on locally compact solvable groups

Details Isoperimetric profile and random walks on locally compact solvable groups Isoperimetric profile and random walks on locally compact solvable groups

2007-06-28

arxiv.org/abs/0706.4257v4

Mathematics

Group Theory

23 pages

Scientific paper

We study a large class of amenable locally compact groups containing 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 which are likely to be only satisfied by these groups.

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