Random walks on the discrete affine group

Jérémie Brieussel (1) , Ryokichi Tanaka (2) , Tianyi Zheng

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Tohoku University [Sendai]

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.

Domaines: Mathématiques [math]

Jérémie Brieussel, Ryokichi Tanaka, Tianyi Zheng. Random walks on the discrete affine group. Groups, Geometry, and Dynamics, 2021, 15 (3), pp.935-963. ⟨10.4171/GGD/616⟩. ⟨hal-02048201⟩