Probability, Ergodic Theory, Mathematical Physics Seminar

Universality of directed polymers in the intermediate disorder regime

Julian Ransford (U Toronto)

Friday, September 22nd, 2023
3:30 PM - 4:30 PM
Hylan 1106A

kn 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 \(\beta\) to depend on the length of the polymer \(2n\), with \(\beta=n^{-\alpha}\) for some \(\alpha<1/4\). 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 \(1/5<\alpha<1/4\), using a kind of “local chaos expansion”.

Event contact: arjun dot krishnan at rochester dot edu