Isoperimetric profile and random walks on locally compact solvable groups

Romain Tessera

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arXiv · 0706.4257

Isoperimetric profile and random walks on locally compact solvable groups

Romain Tessera

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Abstract

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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BibTeX RIS

Romain Tessera. 2010-12-04. Isoperimetric profile and random walks on locally compact solvable groups. https://arxiv.org/abs/0706.4257

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