Carissimi, sono noti gli abstract della giornata di seminari del 15 Dicembre 2017 (secondo incontro della serie di giornate sulla probabilita` e le sue applicazioni alla Fisica, Biologia e Scienze sociali). Ricordo che ciascuno oratore fara` una lezione introduttiva e divulgativa di 45 minuti pensata proprio per i non esperti, seguita da altri 45 minuti di tipo seminario (vedi programma).

Per maggiori informazioni e aggiornamenti sulle giornate passate e future abbiamo istituito una pagina web che vi invitiamo a visitare periodicamente. http://web.math.unifi.it/users/fnardi/seminari/

AN AUTUMN DAY IN PROBABILITY AND STATISTICAL PHYSICS

University of Florence Friday 15 December 2017

Lecturers: Milton Jara (IMPA) and Nikos Zygouras (Warwick)

Location: Aula Magna di Via S. Gallo 10, Firenze

Dr. Milton Jara (IMPA: Istituto de Matematica Pura e Aplicada, Rio de Janeiro, Brasil) Title: Weak universality of the stationary KPZ equation

Abstract: A basic question about Markov chains is the asymptotic behavior of integrals of some function of the chain along its trajectory. In the literature, those integrals are sometimes called 'Birkhoff averages' or 'additive functionals'. In the first talk, I will introduce a general strategy to estimate moment generating functions of these additive functionals in terms of the relative entropy of the chain with respect to carefully constructed reference measures. In the second talk, I will explain how to use this strategy to prove that for a large class of weakly asymmetric stochastic systems, the density of particles is well approximated by the stationary KPZ equation. This proof does not require explicit knowledge of the stationary measures of the stochastic systems, which was a major drawback of previous results.

Dr. Nikos Zygouras (University of Warwick, Coventry, UK) Title: Combinatorial structures in KPZ stochastic models

Abstract: It was proposed by Kardar, Parisi and Zhang in the 1980s that a large class of randomly growing interfaces exhibit universal fluctuations described mathematically by a nonlinear stochastic partial differential equation, which is now known as the Kardar-Parisi-Zhang or KPZ equation. Examples of physical systems which fall in this class are percolation of liquid in porous media, growth of bacteria colonies, currents in one dimensional traffic or liquid systems, liquid crystals etc.

Surprisingly the fluctuations of such random interfaces are governed by exponents and distributions that differ from the predictions given by the classical central limit theorem and in dimension one are linked to laws emerging from random matrix theory. The link between random growth and random matrices (which still demands deeper investigation) is certain combinatorial structures.

In these talks I review the current status of the field and describe some of the combinatorial structures and the advances (both older and more recent) that these have led to.

Program: 11.00-11.45 Introductory lecture: Jara 11.45-12.00 Break 12.00-12.45 Seminar: Jara 13.00-14.30 Lunch 14.30-15.15 Introductory lecture: Zygouras 15.15-15.30 Break 15.30-16.15 Seminar: Zygouras

Organizers: F. Caravenna N. Cancrini E.N.M. Cirillo P. Dai Pra A. De Masi D. Fanelli F. Flandoli C. Giardina` R. Livi F. Martinelli I.G. Minelli F.R. Nardi E. Presutti B. Scoppola E. Scoppola

Note pratiche: 1) E` importante prenotare il biglietto del treno il piu` presto possibile per poter usufruire di sconti!!!! 2) Stiamo prenotando un ristorante con un paio di menu fissi che possa ospitarci, ma ho bisogno del numero di persone che vogliono mangiare insieme. A coloro che fossero interessati chiedo di mandare un email a francescaromana.nardi@unifi.it Resta fermo il fatto che saremo in pieno centro di Firenze, quindi ci sono moltissime altre possibilita` per mangiare se preferite regolarvi indipendentemente.

Vi aspettiamo numerosi Francesca R. Nardi

Dipartimento di Matematica e Informatica Università degli Studi di Firenze Viale Morgagni 67, Firenze, Italy