Universality of directed polymers in the intermediate disorder regime
Speaker:
Julian Ransford, University of Toronto
Date and Time:
Monday, April 24, 2023 - 3:00pm to 4:00pm
Location:
Fields Institute, Room 210
Abstract:
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”.