Random Walks on Lie Groups

  • Harry Furstenberg
Part of the Mathematical Physics and Applied Mathematics book series (MPAM, volume 5)


We present in this paper a limited selection of topics intended to introduce the reader to the subject of random walks on Lie groups. The selection has been highly individual and makes no pretense of completeness. For a more comprehensive view of the area the reader should consult [1,8–10].


Random Walk Irreducible Representation Maximal Compact Subgroup Boundary Space Riemannian Symmetric Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Azencott, R., Espaces de Poisson des Groupes Localement Compacts, Lecture Notes in Math. 148, Springer, 1970.Google Scholar
  2. [2]
    Brunel, A., Crepel, P., Guivarc’h, Y., and Keane, M., ‘Marches aleatores récurrentes sur les groupes localement compacts’, Comptes Rendus 275 (1972).Google Scholar
  3. [3]
    Furstenberg, H., ‘A Poisson formula for semi-simple Lie groups’, Ann. of Math. (2) 77 (1963), 335–386.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Furstenberg, H., ‘Non-commuting random products’, Trans. Amer. Math. Soc. 108 (1963), 377–428.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Furstenberg, H., ‘Boundaries of Riemannian symmetric spaces’, Symmetric Spaces Short courses presented at Washington University, New York, 1972.Google Scholar
  6. [6]
    Furstenberg, H. ‘Boundary theory and stochastic processes on homogeneous spaces’ in Harmonic Analysis on Homogeneous Spaces, Symposia in Pure Math., A.M.S., Williamstown, Mass., 1973.Google Scholar
  7. [7]
    Glasner, S., Proximal Flows, Lecture Notes in Math. 517, Springer, 1976.Google Scholar
  8. [8]
    Grenander, U., Probabilities on Algebraic Structures, Wiley, New York, 1963.MATHGoogle Scholar
  9. [9]
    Guivarc’h, Y., ‘Une loi des grands nombres pour les groupes de Lie’, to appear.Google Scholar
  10. [10]
    Guivarc’h, Y., Keane, M., and Roynette, B., Marches Aléatoires sur les groupes de Lie, Lecture Notes in Math. 624, Springer, 1977.Google Scholar
  11. [11]
    Kingman, J. F. C., ‘Subadditive ergodic theory’, Annals of Probability 1, 883–909.Google Scholar
  12. [12]
    Raugi, A., ‘Fonctions harmoniques sur les groupes localement compacts a base denombable’, Bull. Soc. Math de France (1977)Google Scholar
  13. [13]
    Tits, J., ‘Travaux de Margulis sur les sous-groupes discrets des groupes de Lie’, Séminaire Bourbaki, 1975/76, No. 482.Google Scholar
  14. [14]
    Tutubalin, V. N., ‘Some theorems of the type of the law of large numbers’, Theory of Probability, 1969, pp. 313–319.Google Scholar
  15. [15]
    Zimmer, R., ‘Amenable group actions and an application to Poisson boundaries of random walks’, J. Func. Anal. 27, (1978) 350–372.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1980

Authors and Affiliations

  • Harry Furstenberg
    • 1
  1. 1.Hebrew UniversityJerusalemIsrael

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