Cari colleghi lunedì 8 novembre 2021 riprenderanno i seminari online del Gruppo UMI PRISMA, con i seguenti interventi: * November 8, 2021, 16:00-17:00 (CET): Giovanni Peccati TITLE: Quantitative stabilization results on the Poisson space [1] ABSTRACT: Consider a random variable associated with a random point configuration generated by a Poisson point process (for instance, is the length of some random geometric graph). How can we assess the discrepancy between the distribution of and the one of a Gaussian random variable? The aim of my talk is to describe some recent results in this direction, all relying on some quantitative version of the notion of "geometric stabilization", as formalized by Penrose & Yukich in 2001. In doing so, I will sketch the general philosophy of a powerful collection of techniques for establishing probabilistic approximations, known as the "Malliavin-Stein method". Some explicit examples will be discussed, in particular, related to models of combinatorial optimization and random forests. * November 8, 2021, 17:00-18:00 (CET): Francesco Grotto TITLE: Completely Random Measures and 2D Euler's Equations [1] ABSTRACT: We will recall generalities on completely random measures -alias independently scattered measures- and their natural interaction with divergence-less flows on the underlying domain. We will then proceed to argue how these random fields thus constitute invariant measures for 2d incompressible Euler's equations, outline how a notion of solution to the latter nonlinear dynamics can be given in this setting by means of stochastic integrals, and discuss both rigorous results and open problems relating to the well-posedness of this measure-preserving system. Per altre informazioni: http://www.umi-prisma.polito.it/webinars.html Collegamento Teams: [1] https://teams.microsoft.com/l/meetup-join/19%3a667d2414be564c5d8fba30acffeb8... Grazie per l'attenzione, Domenico Marinucci -- @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ Domenico Marinucci Dipartimento di Matematica Università di Roma Tor Vergata https://www.mat.uniroma2.it/~marinucc/ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@