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). |