Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-19T21:05:55.482Z Has data issue: false hasContentIssue false

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
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
[4] Brofferio, Sara, and Schapira, Bruno: Poisson boundary of GLd (Q), Israel J. Math. 185, (2011), 125–40.Google Scholar
[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).

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×