Carissimi, Vi annunciamo che prossimamente si terrà la nona giornata di seminari: AN ``AUTUMN'' DAY IN PROBABILITY AND STATISTICAL PHYSICS University of Florence Friday 22 November 2019 Lecturers: Sabine Jansen (Munich) and Luca Avena (Leiden) Location: Aula Tricerri Viale Morgagni 67, Firenze Informazioni su come arrivare alla pagina: <https://www.dimai.unifi.it/vp-285-come-arrivare-how-to-get.html> https://www.dimai.unifi.it/vp-285-come-arrivare-how-to-get.html Note pratiche: Stiamo prenotando un catering con cibi vegerariani e non, percio` abbiamo bisogno del numero di persone che vogliono mangiare insieme. A coloro che fossero interessati (per una migliore organizzazione) chiediamo di mandare un email a <mailto:francescaromana.nardi@unifi.it> francescaromana.nardi@unifi.it; <mailto:gianmarco.bet@unifi.it> gianmarco.bet@unifi.it; <mailto:angela.caporicci@unifi.it> angela.caporicci@unifi.it con l'intenzione di partecipare al seminario, al coffe break e al pranzo. PROGRAMMA Prof. Sabine Jansen (LMU Munich) Title: Large deviations and metastability for the Widom-Rowlinson model Abstract: The Widom-Rowlinson model is one of the few models in statistial mechanics for which a phase transition is rigorously proven. It is also popular in stochastic geometry and spatial statistics where it is called area interaction model and belongs to the broader class of quermass interaction models. After reviewing some relevant background about Gibbs measures for continuum interacting particle systems, I will discuss large deviations for the Widom-Rowlinson model in a joint high-density / low-temperature limit. I will also discuss metastability for a spatial birth and death process, a.k.a. continuum Glauber or grand-canonical Monte-Carlo, for which the Gibbs measure is reversible. Based on joint work with Frank den Hollander, Roman Kotecký and Elena Pulvirenti. Prof. Luca Avena (University of Leiden) Title: Explorations of networks through random spanning forests: theory and applications Abstract: David Wilson in the 1990s described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and, more generally, weighted rooted trees or forests spanning a given graph. The goal of this lecture is to describe the resulting probability measure when Wilson's algorithm is used to sample rooted spanning forests. This forest-measure has a rich, flexible and explicit mathematical structure which makes it a powerful tool to design different algorithms to explore a given network. In the first part of the lecture, I will focus on fundamental aspects of this measure and how it relates to other objects of interest in statistical physics such as the well known Random-cluster model. I will in particular describe the main properties of related observables (e.g. set of roots, induced partition) which turn out to be determinantal processes with simple kernels and then discuss some progress in understanding related scaling limits. The second part of the lecture will be devoted to applications. In particular, depending on time, I plan to discuss four different algorithms aiming at: (1) sampling well-distributed points in a graph, (2) coarse-graning a given network, (3) processing signals on graphs (a novel gaph wavelet transform), (4) estimating the spectrum of the graph Laplacian. The core of this lecture is based on different joint collaborations with the following colleagues and students: Castell, Gaudillere, Melot, Milanesi (Marselle), Quattropani (Rome), Driessen, Koperberg, Magrini (Leiden) , Amblard, Barthelme, Tremblay (Grenoble). Program: 11.00-11.45 Introductory lecture: Jansen 11.45-12.00 Break 12.00-12.45 Seminar: Jansen 13.00-14.30 Lunch 14.30-15.15 Introductory lecture: Avena 15.15-15.30 Break 15.30-16.30 Seminar: Avena Organizers: G. Bet, F. Caravenna, N. Cancrini, E.N.M. Cirillo, F. Colomo, 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. Ricordiamo che ciascun 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). Maggiori informazioni e aggiornamenti sono reperibili alle pagine web http://web.math.unifi.it/users/fnardi/seminari/ o http://silicio.math.unifi.it/wordpress/probability/days-in-probability-and-s... Vi aspettiamo numerosi Gianmarco Bet e Francesca R. Nardi Dipartimento di Matematica e Informatica Università degli Studi di Firenze Viale Morgagni 67, Firenze, Italy