Poisson boundary of triangular matrices in a number field

Bruno Schapira[1]

  • [1] Université Paris-Sud Département de Mathématiques Bât. 425 91405 Orsay Cedex (France)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 2, page 575-593
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Schapira, Bruno. "Poisson boundary of triangular matrices in a number field." Annales de l’institut Fourier 59.2 (2009): 575-593. <http://eudml.org/doc/10405>.

@article{Schapira2009,
abstract = {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.},
affiliation = {Université Paris-Sud Département de Mathématiques Bât. 425 91405 Orsay Cedex (France)},
author = {Schapira, Bruno},
journal = {Annales de l’institut Fourier},
keywords = {Random walks; Poisson boundary; triangular matrices; number field; Bruhat decomposition; random walks},
language = {eng},
number = {2},
pages = {575-593},
publisher = {Association des Annales de l’institut Fourier},
title = {Poisson boundary of triangular matrices in a number field},
url = {http://eudml.org/doc/10405},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Schapira, Bruno
TI - Poisson boundary of triangular matrices in a number field
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 2
SP - 575
EP - 593
AB - 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.
LA - eng
KW - Random walks; Poisson boundary; triangular matrices; number field; Bruhat decomposition; random walks
UR - http://eudml.org/doc/10405
ER -

References

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  3. D. I. Cartwright, V. A. Kaimanovich, W. Woess, Random walks on the affine group of local fields and of homogeneous trees, Ann. Inst. Fourier 44 (1994), 1243-1288 Zbl0809.60010MR1306556
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  9. Y. Guivarc’h, A. Raugi, Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete 69 (1985), 187-242 Zbl0558.60009MR779457
  10. V. A. Kaimanovich, The Poisson formula for groups with hyperbolic properties, Ann. of Math. 152 (2000), 659-692 Zbl0984.60088MR1815698
  11. S. Lang, Introduction to diophantine approximations, (1966), Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. Zbl0144.04005MR209227
  12. F. Ledrappier, Poisson boundaries of discrete groups of matrices, Israel J. Math. 50 (1985), 319-336 Zbl0574.60012MR800190
  13. A. Raugi, Fonctions harmoniques sur les groupes localement compacts à base dénombrable, Bull. Soc. Math. France Mém. (1977), 5-118 Zbl0389.60003MR517392
  14. P. Samuel, Théorie algébrique des nombres, (1967), Hermann, Paris Zbl0146.06402MR215808
  15. J.-P. Serre, Corps locaux, (1968), Hermann, Paris Zbl0423.12017MR354618
  16. G. Warner, Harmonic analysis on semi-simple Lie groups. I, 188 (1972), Springer-Verlag, New York-Heidelberg Zbl0265.22020MR498999
  17. A. Weil, Basic number theory, 144 (1974), Springer-Verlag, New York-Berlin Zbl0326.12001MR427267

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