Thumbnail - No thumbnail

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

Type
Article accepté pour publication ou publié
External document link
http://fr.arxiv.org/abs/1303.4042
Date
2013
Journal name
Electronic Journal of Probability
Volume
18
Pages
art 78
Publication identifier
Metadata
Show full item record
Author(s)
Einav, Amit
Carrapatoso, Kleber
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 / Keywords
Entropic Stability; Entropic Chaos; Entropy; Kac's model; Local Lévy central theorem