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Random walks on the discrete affine group
Groups, Geometry, and Dynamics ( IF 0.6 ) Pub Date : 2021-08-03 , DOI: 10.4171/ggd/616 Jérémie Brieussel 1 , Ryokichi Tanaka 2 , Tianyi Zheng 3
Groups, Geometry, and Dynamics ( IF 0.6 ) Pub Date : 2021-08-03 , DOI: 10.4171/ggd/616 Jérémie Brieussel 1 , Ryokichi Tanaka 2 , Tianyi Zheng 3
Affiliation
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.
中文翻译:
离散仿射群上的随机游走
我们引入正则树的离散仿射群作为仿射群的有限生成子群。我们将其上随机游走的泊松边界描述为配置空间。我们计算组的等周剖面和希尔伯特压缩指数。我们还讨论了与一些点灯者组和点灯者图的度量关系。
更新日期:2021-10-07
中文翻译:
离散仿射群上的随机游走
我们引入正则树的离散仿射群作为仿射群的有限生成子群。我们将其上随机游走的泊松边界描述为配置空间。我们计算组的等周剖面和希尔伯特压缩指数。我们还讨论了与一些点灯者组和点灯者图的度量关系。