Abstract:
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).
Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica, L.go S. L. Murialdo 1 - Aula 211
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