English
Multiple ergodic theorems: old and new - Lecture 1
Post-edited
Auteurs : Kra, Bryna (Auteur de la Conférence)
CIRM (Editeur )
37A05 - Measure-preserving transformations
37A15 - General groups of measure-preserving transformations
37A25 - Ergodicity, mixing, rates of mixing
CIRM (Editeur )
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| ergodic theorem multiple recurrence multiple convergence multiple polynomial convergence Walsh's theorem |
Résumé :
The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.
Codes MSC : 37A05 - Measure-preserving transformations
37A15 - General groups of measure-preserving transformations
37A25 - Ergodicity, mixing, rates of mixing
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 14/12/16 Date de captation : 07/12/16 Sous collection : Research talks arXiv category : Dynamical Systems ; Number Theory Domaine : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:01:51 Audience : Researchers Download : https://videos.cirm-math.fr/2016-12-07_Kra_part1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Probabilistic aspects of multiple ergodic averages / Aspects probabilistes des moyennes ergodiques multiplesOrganisateurs de la rencontre : Chazottes, Jean-René ; Kraaikamp, Cor ; Redig, Frank Dates : 05/12/16 - 09/12/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1512.html
Données de citation
DOI : 10.24350/CIRM.V.19098803Citer cette vidéo: Kra, Bryna (2016). Multiple ergodic theorems: old and new - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19098803 URI : http://dx.doi.org/10.24350/CIRM.V.19098803 |
Voir aussi
- [Multi angle] Operators in ergodic theory - Lecture 3: Compact semigroups and splitting theorems / Auteur de la Conférence Haase, Markus.
- [Multi angle] Operators in ergodic theory - Lecture 2: Dilations and joinings / Auteur de la Conférence Haase, Markus.
- [Multi angle] Operators in ergodic theory - Lecture 1: Operators dynamics versus base space dynamics / Auteur de la Conférence Haase, Markus.
- [Multi angle] Multiple ergodic theorems: old and new - Lecture 3 / Auteur de la Conférence Kra, Bryna.
- [Multi angle] Multiple ergodic theorems: old and new - Lecture 2 / Auteur de la Conférence Kra, Bryna.
Bibliographie
- Host, B., & Kra, B. (2005). Nonconventional ergodic averages and nilmanifolds. Annals of Mathematics Second Series, 161(1), 397-488 - http://dx.doi.org/10.4007/annals.2005.161.397
- Host, B., & Kra, B. (2005). Convergence of polynomial ergodic averages. Israel Journal of Mathematics, 149, 1-19 - http://dx.doi.org/10.1007/BF02772534
- Leibman, A. (2005). Convergence of multiple ergodic averages along polynomials of several variables. Israel Journal of Mathematics, 146, 303-315 - http://dx.doi.org/10.1007/BF02773538
- Walsh, M.N. (2012). Norm convergence of nilpotent ergodic averages
Annals of Mathematics Second Series, 175(3), 1667-1688 - http://dx.doi.org/10.4007/annals.2012.175.3.15
