In this talk, we consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the partition function. It was proven by Comets and Liu that for sufficiently high temperature, the fluctuations converge in distribution towards the product of the limiting partition function and an independent Gaussian random variable. We extend the result to the whole L^2-region, which is predicted to be the maximal high-temperature region where the Gaussian fluctuations should occur under the considered scaling. This is joint work with Clément Cosco.
Shuta Nakajima is a postdoctoral researcher at Nagoya University. He earned his Ph.D. from Kyoto University. His main research interests focus on First-passage percolation and Directed polymer.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai