Dynamical Systems
Discretization of harmonic measures for foliated bundles
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 621-626.

We prove in this Note that there is, for some foliated bundles, a bijective correspondence between Garnettʼs 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.

On prouve dans cette Note quʼil y a, pour certains fibrés feuilletés, une correspondance bijective entre les mesures harmoniques au sens de Garnett et les mesures sur la fibre qui sont stationnaires pour une certaine mesure de probabilité sur le groupe dʼholonomie. Nous en déduisons lʼunicité de la mesure harmonique pour certains feuilletages transverses à une fibration projective.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.06.010
Alvarez, Sébastien 1

1 Institut de mathématiques de Bourgogne, CNRS-UMR 5584, Université de Bourgogne, 21078 Dijon cedex, France
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Alvarez, Sébastien. Discretization of harmonic measures for foliated bundles. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 621-626. doi : 10.1016/j.crma.2012.06.010. http://www.numdam.org/articles/10.1016/j.crma.2012.06.010/

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