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arXiv · 1703.07741

Random walks on the discrete affine group

Jérémie Brieussel·Ryokichi Tanaka·Tianyi Zheng
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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.

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Jérémie Brieussel, Ryokichi Tanaka, Tianyi Zheng. 2017-03-22. Random walks on the discrete affine group. https://arxiv.org/abs/1703.07741

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