Isoperimetric profile and random walks on locally compact solvable\n groups

2007/06/28 by Romain Tessera, Tessera, Romain · 2 citations
Mathematics · #advanced mathematical theories #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0706.4257

Abstract

We study a large class of amenable locally compact groups containing all\nsolvable algebraic groups over a local field and their discrete subgroups. We\nshow that the isoperimetric profile of these groups is in some sense optimal\namong amenable groups. We use this fact to compute the probability of return of\nsymmetric random walks, and to derive various other geometric properties which\nare likely to be only satisfied by these groups.\n

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• Obstructions for quantitative measure equivalence between locally compact groups
• Isoperimetric profiles of lamplighter-like groups

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