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4 - A Construction of the Measurable Poisson Boundary: From Discrete to Continuous Groups

Published online by Cambridge University Press:  20 July 2017

Sara Brofferio
Affiliation:
Université Paris-Sud, Laboratoire de Mathématiques et IUT de Sceaux, 91405 Orsay Cedex, France
Tullio Ceccherini-Silberstein
Affiliation:
Università degli Studi del Sannio, Italy
Maura Salvatori
Affiliation:
Università degli Studi di Milano
Ecaterina Sava-Huss
Affiliation:
Cornell University, New York
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Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] Babillot, Martine: An introduction to Poisson boundaries of Lie groups. Probability measures on groups: recent directions and trends, 1–90, Tata Inst. Fund. Res., Mumbai, 2006.
[2] Breuillard, Emmanuel: Equidistribution of random walks on nilpotent Lie groups and homogeneous spaces. Thesis (PhD)- Yale University. ProQuest LLC, Ann Arbor, MI, 2004. 162 pp.
[3] Brofferio, Sara: The Poisson boundary of random rational affinities, Ann. Inst. Fourier 56, (2006), 499–515.Google Scholar
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[5] Derriennic, Yves: Entropie, théorèmes limite et marches aléatoires, in Probability measures on groups VIII (Oberwolfach, 1985), LNM 1210, pp. 241–84, Springer, Berlin (1986).Google Scholar
[6] Elie, Laure: Noyaux potentiels associés aux marches aléatoires sur les espaces homogènes. Quelques exemples clefs dont le groupe affine, in Théorie du potentiel (Orsay, 1983), volume 1096 of Lectures Notes in Math., 223–60, Springer, Berlin, 1984.
[7] Furman, Alex: Random walks on groups and random transformations, Handbook of dynamical systems, vol. 1A, pp. 931–1014, Amsterdam: North-Holland (2002).
[8] Furstenberg, H.: A Poisson formula for semi-simple Lie groups, Ann. of Math. 77 (1963), 335–86.Google Scholar
[9] Furstenberg, H.: Boundary theory and stochastic processes on homogeneous spaces, in Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), pp. 193–229, Amer. Math. Soc., Providence, R.I. (1973).
[10] Guivarc'h, Yves: Extension d'un théorème de Choquet-Deny à une classe de groupes non abéliens Séminaire KGB sur les Marches Aléatoires (Rennes, 1971–1972) 41–59. Astérisque, 4, Soc. Math. France, Paris, 1973.
[11] Guivarc'h,, Yves: Quelques proprits asymptotiques des produits de matrices alatoires. (French) Eighth Saint Flour Probability Summer School–1978 (Saint Flour, 1978), pp. 177–250, Lecture Notes in Math., 774, Springer, Berlin, 1980.
[12] Guivarc'h, Y., and Raugi, A.: Frontière de Furstenberg, proprétés de contraction et thórèmes de convergence.
[13] Kaimanovich, V. A.: The Poisson formula for groups with hyperbolic properties, Ann. of Math. (2) 152, (2000), 659–92.Google Scholar
[14] Kaimanovich, V. A.: Lyapunov exponents, symmetric spaces and a multiplicative ergodic theorem for semisimple Lie groups, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 164 (1987), Differentsialnaya Geom. Gruppy Li i Mekh. IX, 29–46, 196–97; translation in J. Soviet Math. 47 (1989), no. 2, 2387–98.Google Scholar
[15] Kaimanovich, V. A. and Vershik, A. M.: Random walks on discrete groups: boundary and entropy, Ann. Probab. 11, (1983), 457–90.Google Scholar
[16] Quint, J-F: Choquet-Deny theorem for critical measures on the group ax + b, Unpublished
[17] Raugi, Albert: Fonctions harmoniques sur les groupes localement compacts base dnombrable. (French) Bull. Soc. Math. France Mm. No. 54 (1977), 5–118.Google Scholar
[18] Raugi, Albert: Périodes des fonctions harmoniques bornées, Seminar on Probability, Rennes 1978 (French), Exp. No. 10, 16, Univ. Rennes, Rennes (1978).
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