Français
Multiple ergodic theorems: old and new - Lecture 1
Post-edited
Authors : Kra, Bryna (Author of the conference)
CIRM (Publisher )
37A05 - Measure-preserving transformations
37A15 - General groups of measure-preserving transformations
37A25 - Ergodicity, mixing, rates of mixing
CIRM (Publisher )
Loading the player...
|
| ergodic theorem multiple recurrence multiple convergence multiple polynomial convergence Walsh's theorem |
Abstract :
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.
MSC Codes : 37A05 - Measure-preserving transformations
37A15 - General groups of measure-preserving transformations
37A25 - Ergodicity, mixing, rates of mixing
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/12/16 Conference Date : 07/12/16 Subseries : Research talks arXiv category : Dynamical Systems ; Number Theory Mathematical Area(s) : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:01:51 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-12-07_Kra_part1.mp4 
|
Information on the Event
Event Title : Probabilistic aspects of multiple ergodic averages / Aspects probabilistes des moyennes ergodiques multiplesEvent Organizers : Chazottes, Jean-René ; Kraaikamp, Cor ; Redig, Frank Dates : 05/12/16 - 09/12/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1512.html
Citation Data
DOI : 10.24350/CIRM.V.19098803Cite this video as: 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 |
See Also
- [Multi angle] Operators in ergodic theory - Lecture 3: Compact semigroups and splitting theorems / Author of the conference Haase, Markus.
- [Multi angle] Operators in ergodic theory - Lecture 2: Dilations and joinings / Author of the conference Haase, Markus.
- [Multi angle] Operators in ergodic theory - Lecture 1: Operators dynamics versus base space dynamics / Author of the conference Haase, Markus.
- [Multi angle] Multiple ergodic theorems: old and new - Lecture 3 / Author of the conference Kra, Bryna.
- [Multi angle] Multiple ergodic theorems: old and new - Lecture 2 / Author of the conference Kra, Bryna.
Bibliography
- 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
