Discretization of harmonic measures for foliated bundles

2012/06/25 by Sébastien Alvarez, Alvarez Sébastien, Sébastien, Alvarez
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1206.5690

7 pages, to appear in Comptes Rendus de l'Académie des Sciences

arxiv created 2012/06/25 · openalex publication_date 2012/06/25 · arxiv updated 2012/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove in this note that there is, for some foliated bundles, a bijective correspondance between Garnett's harmonic measures and measures on the fiber that are stationary for some probability measure on the holonomy group. As a consequence, we show the uniqueness of the harmonic measure in the case of some foliations transverse to projective fiber bundles.

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