Carissimi,
stiamo preparando la prossima giornata di seminari del 16 Marzo 2018 (terzo 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/


A WINTER DAY IN PROBABILITY AND STATISTICAL PHYSICS

University of Florence
Friday 16 March 2018

Lecturers: Frank den Hollander  (Leiden) and Giovanni Peccati (Luxenbourg)

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

Prof. Frank den Hollander (Leiden University)

Title: Large deviations for the Wiener sausage

Abstract: The Wiener sausage is the 1-environment of Brownian motion. It is an important mathematical object because it is one of the simplest non-Markovian functionals of Brownian motion. The Wiener sausage has been studied intensively since the 1970's. It plays a key role in the study of various stochastic phenomena, including heat conduction, trapping in random media, spectral properties of random Schrödinger operators, and Bose-Einstein condensation. In these lectures we look at two specific quantities: the volume and the capacity. After an introduction to the Wiener sausage, we show that both the volume and the capacity satisfy a downward large deviation principle. We identify the rate and the rate function, and analyse the properties of the rate function. We also explain how the large deviation principles are proved with the help of the skeleton approach. Joint work with Michiel van den Berg (Bristol) and Erwin Bolthausen (Zurich). 

Giovanni Peccati (University of Luxembourg)

Title: Stein's method and stochastic geometry

Abstract: The so-called 'Stein's method' for probabilistic approximations is a collection of powerful analytical techniques, allowing one to explicitly assess the distance between the distributions of two random objects, by using caracterizing differential operators. Originally developed by Ch. Stein at the end of the sixties for dealing with one-dimensional normal approximations under weak dependence assumptions, Stein's method has rapidly become a crucial tool in many areas of modern stochastic analysis, ranging from random matrix theory and random graphs, to mathematical physics, geometry, combinatorics and statistics. In the first part of my talk, I will provide a self-contained introduction to Stein's method for normal approximations, by focussing on some connection with generalised integration by parts formulae, both in a continuous and discrete setting. In the second part of my talk, I will present some recent applications of Stein's method in stochastic geometry, with specific emphasis on the geometry of random fields, and on random geometric graphs.

 
Program:
11.00-11.45 Introductory lecture: den Hollander
11.45-12.00 Break
12.00-12.45 Seminar: den Hollander
13.00-14.30 Lunch
14.30-15.15 Introductory lecture: Peccati
15.15-15.30 Break
15.30-16.15 Seminar: Peccati

Organizers:
F. Caravenna, N. Cancrini, E.N.M. Cirillo, P. Dai Pra, A. De Masi, D. Fanelli, F. Flandoli
C. Giardina`, R. Livi, D. Marinucci, 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 (di cui uno vegerariano) 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