Probability in Mathematical Physics 

Cédric Bernardin (Université Côte d'Azur)

2PM, at Room 3.10 Mathematics department IST, Lisbon

Macroscopic fluctuations theory for Ginzburg-Landau dynamics with long range interactions

Abstract
Ginzburg-Landau (GL) dynamics are popular interacting particle systems. Macroscopic fluctuations theory (MFT) is now considered as the cornerstone of non-equilibrium statistical mechanics for diffusive systems. In this talk I will consider GL dynamics with long range interactions so that the system is superdiffusive and hydrodynamic limits are given by (non-linear) fractional diffusion equations. I will discuss issues concerning the establishment of a MFT for these GL dynamics. Joint work with R. Chetrite, P. Gonçalves and M.Jara.

Persi Diaconis (Stanford University )

2PM, at Room 3.10 Mathematics department IST, Lisbon

Gambler's Ruin With Three Gamblers

Abstract
Imagine three gambler's with respectively A, B, C $ at the start. Each time, a pair of gambler's are chosen (uniformly at random) and a fair coin is flipped. Of course, eventually, one of the gambler's is eliminated and the game continues with the remaining two until one winds up with all A+B+C. In poker tournaments (really) it is of interest to know the chances of the six possible elimination orders (eg 3,1,2 means gambler 3 is eliminated first, then gambler 1, leaving 2 with  all the cash). In particular, how do these depend on A,B,C? For small A,B,C, exact computation is possible, but for A,B,C of practical interest, asymptotics are needed. The math involved is surprising; Whitney and John Domains, Carlesson estimates. To test your intuition, recall that if there are two gamblers with 1 and N-1 $. The chance that the first winds up with all N is  1/N. With three gamblers with 1,1 and N-2 the chance that the third is eliminated first is const/ N^3. We don't know the answer for four gamblers. This is a report of joint work with Stew Ethier, Kelsey Huston-Edwards and Laurent Saloff-Coste.

André Schlichting (University of Münster)

2PM, at Room 3.10 Mathematics department IST, Lisbon

Abstract
TBA

Gerardo Barrera Vargas, (University of Helsinki)

2PM, at Room 3.10 Mathematics department IST, Lisbon

Abstract
TBA

Kohei Susuki (Durham University)

2PM, at Room 3.10 Mathematics department IST, Lisbon

Dyson Brownian Motion as a Wasserstein Gradient Flow

Abstract
The Dyson Brownian motion (DMB) is a system of infinitely many interacting Brownian motions with logarithmic interaction potential,

 which was introduced by Freeman Dyson '62 in relation to the random matrix theory. In this talk, we reveal that an infinite-dimensional differential structure induced by the DBM has a Bakry-Émery lower Ricci curvature bound. As an application, we show that the DBM can be realized as the unique Wasserstein-type gradient flow of the Boltzmann-Shannon entropy associated with sine_beta ensemble.

Pedro Paulo Gondim Cardoso (University of Lisbon)

2PM, at Room 3.10 Mathematics department IST, Lisbon

Abstract
TBA

Rajeev Singh (Stony Brook University, New York and West University of Timisoara, Romania)

2PM, online

Abstract
TBA