Geodesic
Random walks on the discrete affine group
Jérémie Brieussel1 ; Ryokichi Tanaka2 ; Tianyi Zheng3 orcid
1University of Montpellier, France
2Tohoku University, Sendai, Japan
3University of California, San Diego, La Jolla, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 935-963

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DOI

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.
DOI : 10.4171/ggd/616
Classification : 20-XX, 60-XX
Mots-clés : Affine group of a tree, random walks, Poisson boundary

Jérémie Brieussel  1   ; Ryokichi Tanaka  2   ; Tianyi Zheng  3

1 University of Montpellier, France
2 Tohoku University, Sendai, Japan
3 University of California, San Diego, La Jolla, USA 
Jérémie Brieussel; Ryokichi Tanaka; Tianyi Zheng. Random walks on the discrete affine group. Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 935-963. doi: 10.4171/ggd/616
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     title = {Random walks on the discrete affine group},
     journal = {Groups, geometry, and dynamics},
     pages = {935--963},
     year = {2021},
     volume = {15},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/616/}
}
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