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Chaos and entropic chaos in Kac's model without high moments


 
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1. Title Title of document Chaos and entropic chaos in Kac's model without high moments
 
2. Creator Author's name, affiliation, country Kleber Carrapatoso; Université Paris-Dauphine; France
 
2. Creator Author's name, affiliation, country Amit Einav; University of Cambridge; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Local Lévy central theorem ; Kac's model ; Entropy ; Entropic Chaos ; Entropic Stability
 
3. Subject Subject classification 60F05 ; 70F99 ; 60J75 ; 82B40
 
4. Description Abstract In this paper we present a new local Lévy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying one-particle function that has moments of order $2\alpha$, with $1<\alpha<2$. We also discuss a lower semi continuity result for the relative entropy with respect to our specific family of functions, and use it to show a form of stability property for entropic chaos in our settings.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) A. Einav was supported by ERC grant MATKIT.
 
7. Date (YYYY-MM-DD) 2013-08-27
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2683
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2683
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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