Entropic and Fisher-Information type chaoticity for a family of rescaled states

Speaker: Hagop Tossounian

CMM – Universidad de Chile, Chile

Date: Monday, March 13, 2023 at 12 Santiago time

Abstract:  For a fixed probability measure f , and each N ≥ 2 we introduce an exchangeable random variable obtained from rescaling Y (Law(Y)=f ⊗N ) to the sphere ∑ xj 2 = N. It is known [2] that all the k-marginals of these processes converge weakly to f⊗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 and can be found in https://arxiv.org/abs/2204.05406.

[1] M. Kac. Foundations of kinetic theory. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. III, pages 171–197, Berkeley and Los Angeles, 1956. California U P

[2] Cortez, R., Tossounian, H. On a Thermostated Kac Model with Rescaling. Ann. Henri Poincar ́e 22, 1629–1668 (2021).

Venue: Online via Zoom / Sala seminarios DIM, 5th floor, Beauchef 851
Chair: Gabrielle Nornberg