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  E-mail Message: I thought you might be interested in this item at http://www.worldcat.org/oclc/879641355 Title: Brownian motion on stationary random manifolds Author: Pablo Lessa; François Ledrappier; Mathilde Martinez; Université Pierre et Marie Curie (Paris / 1971-2017); Universidad de la República (Montevideo). Facultad de Ciencias; École doctorale Sciences mathématiques de Paris centre (Paris / 2000-....) Publisher: 2014. OCLC:879641355

  
  

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Brownian motion on stationary random manifolds

Author:	Pablo Lessa; François Ledrappier; Mathilde Martinez; Université Pierre et Marie Curie (Paris / 1971-2017).; Universidad de la República (Montevideo). Facultad de Ciencias.; All authors
Publisher:	2014.
Dissertation:	Thèse de doctorat : Mathématiques : Paris 6 : 2014. Thèse de doctorat : Mathématiques : Universidad de la República (Montevideo). Facultad de Ciencias : 2014.
Edition/Format:	Computer file : Document : Thesis/dissertation : English
Summary:	On introduit le concept d'une variété aléatoire stationnaire avec l'objectif de traiter de façon unifiée les résultats sur les variétés avec un group d'isométries transitif, les variétés avec quotient compact, et les feuilles génériques d'un feuilletage compact. On démontre des inégalités entre la vitesse de fuite, l'entropie du mouvement brownien et la croissance de volume de la variété aléatoire, en généralisant des résultats d'Avez, Kaimanovich, et Ledrappier. Dans la deuxième partie on démontre que la fonction feuille d'un feuilletage compact est semicontinue, en obtenant comme conséquences le théorème de stabilité local de Reeb, une partie du théorème de structure local pour les feuilletages à feuilles compactes d'Epstein, et un théorème de continuité d'Álvarez et Candel. 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.  Read more...
Subjects	Mouvement brownien. Théorie ergodique. Variétés aléatoires View all subjects
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