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Poisson boundaries of discrete groups of matrices

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Abstract

If μ is a probability measure on a countable group there is defined a notion of the Poisson boundary for μ which enables one to represent all bounded μ-harmonic functions on the group. It is shown that for discrete groups of matrices this boundary can be identified with the boundary of the corresponding Lie group.

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Authors and Affiliations

  1. Université de Paris, 23, Avenue du Mesnil, 94210, La Varenne, France

    François Ledrappier

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  1. François Ledrappier
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Ledrappier, F. Poisson boundaries of discrete groups of matrices. Israel J. Math. 50, 319–336 (1985). https://doi.org/10.1007/BF02759763

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  • DOI: https://doi.org/10.1007/BF02759763

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