Cari colleghi i seminari del gruppo UMI Prisma riprenderanno a partire da Novembre con il calendario consueto (primo lunedì del mese, ore 16-18, online su piattaforma Teams). Qui sotto i dettagli del prossimo incontro (Paolo Dai Pra e Alberto Chiarini), grazie per l'attenzione, Domenico Marinucci * November 7, 2022, 16:00-17:00 (CET): Paolo Dai Pra TITLE: Noise-induced periodicity in stochastic dynamics: some examples ABSTRACT: The emergence of periodic behavior in the dynamics of several interacting components is a common pattern of self-organisation in living systems. Rigorous mathematical treatments are still limited to few examples. In this talk we review some of these examples, emphasizing the essential role of the noise in the appearance of regular rhythms. * November 7, 2022, 17:00-18:00 (CET): Alberto Chiarini TITLE: How costly is it for a simple random walk to cover a fraction of amacroscopic body? ABSTRACT: In this talk we aim at establishing large deviation estimates for the probability that a simple random walk on the Euclidean lattice (d>2) covers a substantial fraction of a macroscopic body. It turns out that, when such rare event happens, the random walk is locally well approximated by random interlacements with a specific intensity, which can be used as a pivotal tool to obtain precise exponential rates. Random interlacements have been introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus, and has been since a popular object of study. In the first part of the talk we introduce random interlacements and give a brief account of some results surrounding this object. In the second part of the talk we study the event that random interlacements cover a substantial fraction of a macroscopic body. This allows to obtain an upper bound on the probability of the corresponding event for the random walk. Finally, by constructing a near-optimal strategy for the random walk to cover a macroscopic body, we discuss a matching large deviation lower bound. The talk is based on ongoing work with M. Nitzschner (NYU Courant). Link dei seminari: https://teams.microsoft.com/l/meetup-join/19%3a667d2414be564c5d8fba30acffeb8... -- @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ Domenico Marinucci Dipartimento di Matematica Università di Roma Tor Vergata https://www.mat.uniroma2.it/~marinucc/ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@