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2013 Chaos and entropic chaos in Kac's model without high moments
Kleber Carrapatoso, Amit Einav
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Electron. J. Probab. 18: 1-38 (2013). DOI: 10.1214/EJP.v18-2683


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.


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Kleber Carrapatoso. Amit Einav. "Chaos and entropic chaos in Kac's model without high moments." Electron. J. Probab. 18 1 - 38, 2013.


Accepted: 27 August 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60017
MathSciNet: MR3101644
Digital Object Identifier: 10.1214/EJP.v18-2683

Primary: 60F05
Secondary: 60J75 , 70F99 , 82B40

Keywords: Entropic chaos , Entropic Stability , Entropy , Kac's model , Local Lévy central theorem

Vol.18 • 2013
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