2024-10-04 

@ Vienna

Venue: Boltzmann Hörsaal, Erwin Schrödinger Institut (ESI), Boltzmanngasse 9, 1090 Vienna

Click here for detailed information on directions and public transport: 

Outbound trains  Budapest Keleti  --> Wien Hbf:     07:40  - 10:20     ///     08:40 - 11:20     ///      09:40 - 12:20

==========================

THE TALKS:

13:30-14:20 

Scott Armstrong (Sorbonne Université and NYU Courant )  

Title: Supediffusive CLT for a Brownian motion in a random drift 

Abstract: We consider the long-time behavior of a diffusion process in $\mathbb{R}^d$, advected by a stationary random vector field which is assumed to be divergence-free, have dihedral symmetry in law, and a log-correlated potential. A special case includes the grad-perp of the Gaussian free field (GFF) in two dimensions, and more generally of the logarithmically-correlated Gaussian field (LGF) in higher dimensions. We prove (in a quenched sense) that the variance of the diffusion process at large times $t$ behaves like $2c_* (\log t )^{1/2}$, with a universal prefactor constant $c_*>0$. We also prove a quenched CLT for the process under this superdiffusive scaling. The arguments are based on a rigorous renormalization group method in which we inductively analyze "coarse-grained diffusivities," scale-by-scale. Our analysis leads to sharp homogenization and large-scale regularity estimates on the infinitesimal generator, which are subsequently transferred into quantitative information on the stochastic process. This line of reasoning also applies to other interesting models in mathematical physics, the subject of ongoing work which I will mention time-permitting. Based on joint work with Ahmed Bou-Rabee (Courant/NYU) and Tuomo Kuusi (Helsinki).  

--------------------------------------------

14:30-15:20

Sylvia Serfaty (Sorbonne Université and NYU Courant )

Title: Dipole transition for the two-component plasma 

Abstract: We study the two-dimensional two-component plasma or Coulomb gas with oppositely charged particles.  We consider a suitable truncation of the charges which allows to make sense of the Gibbs measure beyond $\beta=2$ and show a transition between a system of free charges and a system with bound dipoles, as predicted in the original papers of Kosterlitz and Thouless. This is based on joint work with Thomas Leblé and Ofer Zeitouni, and with Jeanne Boursier. 

--------------------------------------------

15:50-16:40

Christoph Aistleitner (TU Graz)

Title: A celebration of Khinchine's law of the iterated logarithm, from a number theorist's perspective 

Abstract:  We celebrate the centennial of Aleksandr Khinchin's paper "Über einen Satz der Wahrscheinlichkeitsrechnung", which marks the historically first appearance of the law of the iterated logarithm. Originally, the result was deeply rooted in analysis and number theory, before it became absorbed into the axiomatic framework of modern probably theory. However, there is a branch of mathematical research which continued to interpret Khinchin's theorem and other probabilistic limit theorems from the perspective of analysis and number theory, and remains active till this day. We discuss the origins of Khinchin's theorem and its historical context. We present different perspectives on the theorem, and then focus on the perspective of lacunary systems of dilated functions and follow the work of Erdös, Kac, Takahashi, Philipp, Berkes, and others on this topic up to present-day research.

==========================

DINNER:

Dinner will be at Pizzeria Riva, Schlickgasse 2, 1090 Vienna from ~ 6pm. 

==========================

HOTELS NEARBY:

Participants who wish to stay overnight in Vienna are kindly asked to make their own arrangements for accommodation. If you need assistance, please contact Astrid (astrid.kollros@univie.ac.at).

Click here for hotels and hostels nearby.