Chaos and Entropic Chaos in Kac's Model Without High Moments
Einav, Amit; Carrapatoso, Kleber (2013), Chaos and Entropic Chaos in Kac's Model Without High Moments, Electronic Journal of Probability, 18, p. art 78. http://dx.doi.org/10.1214/EJP.v18-2683
TypeArticle accepté pour publication ou publié
External document linkhttp://fr.arxiv.org/abs/1303.4042
Journal nameElectronic Journal of Probability
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Abstract (EN)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.
Subjects / KeywordsEntropic Stability; Entropic Chaos; Entropy; Kac's model; Local Lévy central theorem
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