Groups, Geometry, and Dynamics
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Random walks on the discrete affine groupJérémie Brieussel, Ryokichi Tanaka and Tianyi Zheng (1) University of Montpellier, France
(2) Tohoku University, Sendai, Japan
(3) University of California, San Diego, La Jolla, USA
We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert compression exponent of the group. We also discuss metric relationship with some lamplighter groups and lamplighter graphs.
Keywords: Affine group of a tree, random walks, Poisson boundary
Brieussel Jérémie, Tanaka Ryokichi, Zheng Tianyi: Random walks on the discrete affine group. Groups Geom. Dyn. Electronically published on August 3, 2021. doi: 10.4171/GGD/616 (to appear in print)