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.
Cite this article
Jérémie Brieussel, Ryokichi Tanaka, Tianyi Zheng, Random walks on the discrete affine group. Groups Geom. Dyn. 15 (2021), no. 3, pp. 935–963DOI 10.4171/GGD/616