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.
Revised:
Accepted:
DOI: 10.5802/aif.2441
Classification: 22D40, 28D05, 28D20, 60B15, 60J10, 60J50
Keywords: Random walks, Poisson boundary, triangular matrices, number field, Bruhat decomposition
Author's affiliations:
@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}, pages = {575--593}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {2}, year = {2009}, doi = {10.5802/aif.2441}, mrnumber = {2521429}, zbl = {1171.60003}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2441/} }
TY - JOUR TI - Poisson boundary of triangular matrices in a number field JO - Annales de l'Institut Fourier PY - 2009 DA - 2009/// SP - 575 EP - 593 VL - 59 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2441/ UR - https://www.ams.org/mathscinet-getitem?mr=2521429 UR - https://zbmath.org/?q=an%3A1171.60003 UR - https://doi.org/10.5802/aif.2441 DO - 10.5802/aif.2441 LA - en ID - AIF_2009__59_2_575_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.2441/
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