Carissimi,
Vi annunciamo che prossimamente si terrà la decima giornata di seminari (notare la location differente dal solito!) :
A WINTER DAY IN PROBABILITY AND STATISTICAL PHYSICS
University of Florence Friday 6 March 2020
Lecturers: Massimiliano Gubinelli (Bonn) and Julia Komjathy (Eindhoven)
Location: Aula Magna 327 Viale Morgagni 40, Firenze Link alla mappa: https://goo.gl/maps/zpsC9oGMeqw695jGA
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 francescaromana.nardi@unifi.it; gianmarco.bet@unifi.it; angela.caporicci@unifi.it con l'intenzione di partecipare al seminario, al coffe break e al pranzo.
PROGRAMMA Prof. Massimiliano Gubinelli (Hausdorff Center for Mathematics)
Title: Universality in slow growth phenomena and singular martingale problems
Abstract: In the last years there have been steady progress in understanding the large scale properties of one dimensional growing interfaces. In the regime where the growth is comparable to thermal fluctuations the interface are described via the Kardar-Parisi-Zhang equation (KPZ). This is a stochastic partial differential equation which contains a non-linearity whose precise meaning is not apriori clear. There are various analytic approaches to make sense of such an equation like regularity structures, paracontrolled distributions, rough paths. In this talk we will describe a further approach to the KPZ equation based on the probabilistic notion of martingale problem. This approach can be used to prove the scaling limit of interface fluctuations in a wide class of models. Due to the singular nature of the equation, the martingale problem has to be formulated in a non-standard way and several new ideas are needed to obtain a mathematically satisfactory theory. The aim of the first part of talk will be to give a wide perspective on the phenomenon of universality of the KPZ and related equations and in the issues involved in their definition. In the second part we will discuss more in details the well-posedness of the martingale problem, in particular the uniqueness problem.
Prof. Julia Komjathy (Eindhoven University of Technology)
Title: How to stop explosion by penalising transmission to hubs
Abstract: In this talk we study the spread of information on infinite inhomogeneous spatial random graphs. We take a scale-free spatial random graph, where the degree of a vertex follows a power law with exponent tau >1. Examples of such graphs include: Scale free percolation, Geometric Inhomogeneous Random Graphs, and Hyperbolic Random Graphs. Then we equip each edge with a random and iid transmission delay L, and study the ball-growth of the first-passage infected cluster around the source vertex as a function of time. For a second, more realistic spreading model, the iid random transmission delay L through an edge with expected degrees W and Z is multiplied by a factor that is a polynomial of W,Z, (the penalty factor).
We call the model outwards (inwards) explosive if it is possible to reach infinitely many vertices within finite time (if infinitely many vertices can reach a target vertex within finite time). We will discuss the criterion for explosion in the original model (no penalty factor) and in the penalised model. In particular, we will discuss that asymmetric penalty functions can lead to `outwards' explosion but no `inwards' explosion or the other way round.
Joint work with John Lapinskas and Johannes Lengler.
Program: 11.00-11.45 Introductory lecture: Gubinelli 11.45-12.00 Break 12.00-12.45 Seminar: Gubinelli 13.00-14.30 Lunch 14.30-15.15 Introductory lecture: Komjathy 15.15-15.30 Break 15.30-16.30 Seminar: Komjathy
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 _______________________________________________ Dimai-news mailing list Dimai-news@lists.math.unifi.it https://lists.math.unifi.it/mailman/listinfo/dimai-news