Poisson boundary of triangular matrices in a number field
Annales de l'Institut Fourier, Volume 59 (2009) no. 2, p. 575-593

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary of random rational affinities.

L’objet de cette note est de décrire la frontière de Poisson du groupe des matrices triangulaires supérieures inversibles à coefficients dans un corps de nombre. C’est une généralisation en dimension supérieure d’un résultat de Brofferio concernant la frontière de Poisson du groupe des applications affines rationnelles.

DOI : https://doi.org/10.5802/aif.2441
Classification:  22D40,  28D05,  28D20,  60B15,  60J10,  60J50
Keywords: Random walks, Poisson boundary, triangular matrices, number field, Bruhat decomposition
@article{AIF_2009__59_2_575_0,
     author = {Schapira, Bruno},
     title = {Poisson boundary of triangular matrices in a number field},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {2},
     year = {2009},
     pages = {575-593},
     doi = {10.5802/aif.2441},
     mrnumber = {2521429},
     zbl = {1171.60003},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_2_575_0}
}
Schapira, Bruno. Poisson boundary of triangular matrices in a number field. Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 575-593. doi : 10.5802/aif.2441. http://www.numdam.org/item/AIF_2009__59_2_575_0/

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