Groups, Geometry, and Dynamics

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Published online first: 2021-08-03
DOI: 10.4171/GGD/616

Random walks on the discrete affine group

Jérémie Brieussel[1], Ryokichi Tanaka[2] and Tianyi Zheng[3]

(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)