Random walks on the discrete affine group

J\'er\'emie Brieussel , Ryokichi Tanaka , Tianyi Zheng

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classification 🧮 math.GR math.PR

keywords groupaffinediscretelamplighterrandomwalksboundarycompression

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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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Random walks on the discrete affine group

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