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Brownian motion on stationary random manifolds

Abstract : We introduce the concept of a stationary random manifold with the objective of treating in a unified way results about manifolds with transitive isometry group, manifolds with a compact quotient, and generic leaves of compact foliations. We prove inequalities relating linear drift and entropy of Brownian motion with the volume growth of such manifolds, generalizing previous work by Avez, Kaimanovich, and Ledrappier among others. In the second part we prove that the leaf function of a compact foliation is semicontinuous, obtaining as corollaries Reeb's local stability theorem, part of Epstein's the local structure theorem for foliations by compact leaves, and a continuity theorem of Álvarez and Candel.
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Contributor : Pablo Lessa Connect in order to contact the contributor
Submitted on : Monday, March 17, 2014 - 6:45:14 PM
Last modification on : Sunday, June 26, 2022 - 5:34:40 AM
Long-term archiving on: : Tuesday, June 17, 2014 - 1:57:20 PM


  • HAL Id : tel-00959923, version 3


Pablo Lessa. Brownian motion on stationary random manifolds. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI; Universidad de la República (Montevideo). Facultad de Ciencias, 2014. English. ⟨NNT : 2014PA066050⟩. ⟨tel-00959923v3⟩



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