no. 2
The Poisson boundary of random rational affinities
[La frontière de Poisson des affinités aléatoires à coefficients rationnels]
Annales de l'Institut Fourier, Tome 56 (2006) no. 2, pp. 499-515.

On prouve que pour décrire la frontière de Poisson des affinités à coefficients rationnels est nécessaire et suffisant de considérer l’action sur le corps réel et tous les corps p-adiques.

We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all p-adic fileds.

DOI : https://doi.org/10.5802/aif.2191
Classification : 60B99,  60J50,  43A05,  22E35
Mots clés : frontière de Poisson, marches aléatoires, groupe affine, nombres rationnels, nombres p-adiques 
@article{AIF_2006__56_2_499_0,
     author = {Brofferio, Sara},
     title = {The {Poisson} boundary of random rational affinities},
     journal = {Annales de l'Institut Fourier},
     pages = {499--515},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {56},
     number = {2},
     year = {2006},
     doi = {10.5802/aif.2191},
     mrnumber = {2226025},
     zbl = {1087.60011},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2191/}
}
TY  - JOUR
AU  - Brofferio, Sara
TI  - The Poisson boundary of random rational affinities
JO  - Annales de l'Institut Fourier
PY  - 2006
DA  - 2006///
SP  - 499
EP  - 515
VL  - 56
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2191/
UR  - https://www.ams.org/mathscinet-getitem?mr=2226025
UR  - https://zbmath.org/?q=an%3A1087.60011
UR  - https://doi.org/10.5802/aif.2191
DO  - 10.5802/aif.2191
LA  - en
ID  - AIF_2006__56_2_499_0
ER  - 
Brofferio, Sara. The Poisson boundary of random rational affinities. Annales de l'Institut Fourier, Tome 56 (2006) no. 2, pp. 499-515. doi : 10.5802/aif.2191. http://www.numdam.org/articles/10.5802/aif.2191/

[1] Babillot, Martine; Bougerol, Philippe; Elie, Laure The random difference equation X n =A n X n-1 +B n in the critical case, Ann. Probab., Volume 25 (1997) no. 1, pp. 478-493 | Article | MR 1428518 | Zbl 0873.60045

[2] Bougerol, Philippe; Picard, Nico Strict stationarity of generalized autoregressive processes, Ann. Probab., Volume 20 (1992) no. 4, pp. 1714-1730 | Article | MR 1188039 | Zbl 0763.60015

[3] Brofferio, Sara Poisson boundary for finitely generated groups of rational affinities (Preprint)

[4] Brofferio, Sara Speed of locally contractive stochastic systems, Ann. Probab., Volume 31 (2003) no. 4, pp. 2040-2067 | Article | MR 2016611 | Zbl 1046.60067

[5] Cartwright, D. I.; Kaĭmanovich, V. A.; Woess, W. Random walks on the affine group of local fields and of homogeneous trees, Ann. Inst. Fourier (Grenoble), Volume 44 (1994) no. 4, pp. 1243-1288 | Article | Numdam | MR 1306556 | Zbl 0809.60010

[6] Cassels, J. W. S. Global fields, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 42-84 | MR 222054

[7] Derriennic, Y. Entropie, théorèmes limite et marches aléatoires, Probability measures on groups, VIII (Oberwolfach, 1985) (Lecture Notes in Math.), Volume 1210, Springer, Berlin, 1986, pp. 241-284 | MR 879010 | Zbl 0612.60005

[8] Derriennic, Yves Quelques applications du théorème ergodique sous-additif, Conference on Random Walks (Kleebach, 1979) (French) (Astérisque), Volume 74, Soc. Math. France, Paris, 1980, p. 183-201, 4 | MR 588163 | Zbl 0446.60059

[9] Élie, Laure Noyaux potentiels associés aux marches aléatoires sur les espaces homogènes. Quelques exemples clefs dont le groupe affine, Théorie du potentiel (Orsay, 1983) (Lecture Notes in Math.), Volume 1096, Springer, Berlin, 1984, pp. 223-260 | MR 890360 | Zbl 0571.60076

[10] Furstenberg, Harry Boundary theory and stochastic processes on homogeneous spaces, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), Amer. Math. Soc., Providence, R.I., 1973, pp. 193-229 | MR 352328 | Zbl 0289.22011

[11] Kaĭmanovich, V. A.; Vershik, A. M. Random walks on discrete groups: boundary and entropy, Ann. Probab., Volume 11 (1983) no. 3, pp. 457-490 | Article | MR 1178986 | Zbl 0823.60006

[12] Kaimanovich, Vadim A. Poisson boundaries of random walks on discrete solvable groups, Probability measures on groups, X (Oberwolfach, 1990), Plenum, New York, 1991, pp. 205-238 | MR 1815698 | Zbl 0984.60088

[13] Kaimanovich, Vadim A. The Poisson formula for groups with hyperbolic properties, Ann. of Math. (2), Volume 152 (2000) no. 3, pp. 659-692 | Article | MR 704539 | Zbl 0641.60009

[14] Kesten, Harry Random difference equations and renewal theory for products of random matrices, Acta Math., Volume 131 (1973), pp. 207-248 | Article | MR 440724 | Zbl 0291.60029

[15] Lang, Serge Introduction to diophantine approximations, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966 | MR 209227 | Zbl 0144.04005

[16] Vervaat, Wim On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables, Adv. in Appl. Probab., Volume 11 (1979) no. 4, pp. 750-783 | Article | MR 544194 | Zbl 0417.60073

Cité par Sources :