JournalsggdVol. 15, No. 3pp. 935–963

Random walks on the discrete affine group

  • Jérémie Brieussel

    University of Montpellier, France

  • Ryokichi Tanaka

    Tohoku University, Sendai, Japan

  • Tianyi Zheng

    University of California, San Diego, La Jolla, USA
Random walks on the discrete affine group cover
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Abstract

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. 935–963

DOI 10.4171/GGD/616