Talks Monday

[Balint Virag]

Dear All,

Tomorrow (Monday, April 24) we will have two talks, by our own Andras
Meszaros and Julian Ransford.

Also, let me know if you are interested in joining for lunch! Or just
meet us at 12:30 on the ground floor of Bahen, at the south elevators.

Balint


Eigenvectors of the square grid plus GUE

Starts: 14:10 on Monday April 24, 2023
Ends: 15:00 on Monday April 24, 2023
Location: FI210, Fields Institute, 222 College St.

Andras Meszaros

Eigenvectors of the GUE-perturbed discrete torus with uniform boundary
conditions retain some product structure for small perturbations but
converge to discrete Gaussian waves for large perturbations. We
determine where this phase transition happens. Joint work with Balint Virag.


Universality of directed polymers in the intermediate disorder regime

Starts: 15:10 on Monday April 24, 2023
Ends: 16:00 on Monday April 24, 2023
Location: FI210, Fields Institute, 222 College St.

Julian Ransford

In 2018, Krishnan and Quastel showed that the fluctuations of
Seppäläinen's log-gamma polymer converge in law to the Tracy-Widom GUE
distribution in the intermediate disorder regime. This regime
corresponds to taking the inverse temperature β to depend on the length
of the polymer 2n, with β=n−α for some exponent α<1/4. They also
conjectured that this should hold for directed polymers with general
i.i.d weights. In this talk, I will sketch a proof of their conjecture
for 1/5<α<1/4, using a kind of “local chaos expansion”.