Discretization of harmonic measures for foliated bundles
Alvarez S\'ebastien
TL;DR
This paper establishes a correspondence between harmonic measures and stationary measures on fibers for certain foliated bundles, leading to results on the uniqueness of harmonic measures in specific foliations.
Contribution
It introduces a bijective correspondence between harmonic measures and stationary measures on fibers for some foliated bundles, and proves uniqueness in particular cases.
Findings
Established a bijective correspondence between harmonic and stationary measures.
Proved the uniqueness of harmonic measures for certain foliations.
Connected harmonic measures with measures on fibers via holonomy group actions.
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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Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Mathematical Dynamics and Fractals