Seminari del Dipartimento

 

Fisica Matematica

Entropic chaoticity and Fisher information type chaoticity for a family of rescaled states (j. w. Roberto Cortez)

Hagop Tossounian


17-05-2022 - 16:30
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211

 

For a probability measure $f$, and each $N >=2$ we introduce an exchangeable random variable obtained from rescaling Y (Law(Y)= $f^{otimes N}$) to the sphere $sum {x_j}^2 = N$. It is known [2] that all the k-marginals of these processes converge weakly to $f^{otimes k}$,(a property known as chaoticity and used by Mark Kac [1]). The aim of the talk is to show that the chaos property of this sequence of rescaled r.v. can be strengthened to entropic chaos and to Fisher-information chaos, under mild assumptions on $f$. This work is j.w. Roberto Cortez arXiv:2204.05406. [1] Kac M.Foundations of Kinetic Theory. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954 − 1955, vol. III, pp. 171–197. University of California Press, Berkeley and Los Angeles, 1956. [2] Cortez, R., Tossounian, H. On a Thermostated Kac Model with Rescaling. Ann. Henri Poincaré 22, 1629–1668 (2021).
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