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.
Cite this article
Romain Tessera, Isoperimetric profile and random walks on locally compact solvable groups. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 715–737DOI 10.4171/RMI/736