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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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.

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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