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On the regularity of stationary measures

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Abstract

Extending a construction of Bourgain for SL(2,R), we construct on any semisimple real Lie group G a symmetric probability measure whose stationary measure on the Furstenberg boundary has a smooth density and whose support is finite and generates a dense subgroup of G.

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Authors and Affiliations

  1. Institut de mathématique d’Orsay, UMR 8628 CNRS, Université Paris-Sud, Bât. 307, F-91405, Orsay Cedex, France

    Yves Benoist

  2. CNRS—Université Bordeaux I, 33405, Talence, France

    Jean-François Quint

Authors
  1. Yves Benoist
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  2. Jean-François Quint
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Correspondence to Yves Benoist.

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Benoist, Y., Quint, JF. On the regularity of stationary measures. Isr. J. Math. 226, 1–14 (2018). https://doi.org/10.1007/s11856-018-1689-x

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  • DOI: https://doi.org/10.1007/s11856-018-1689-x

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