Abstract:
The directed polymer model describes the evolution of directed paths affected by a random medium. It has attracted much interest recently because the random interface defined from its partition function is expected to lie in the KPZ universality class, i.e., it is governed by universal scaling exponents. We discuss the case of spatial dimension d > 2, where a phase transition occurs between a weak disorder regime at high temperature (polymer paths behave like Brownian motion) and a strong disorder regime at low temperature (polymer paths concentrate in a microscopically small region where the medium is ”favorable”). We discuss some recent results about the behavior in the weak disorder phase close to the critical point, specifically, the integrability of the partition function and the so-called local limit theorem.
Biography:
Stefan Junk is an Assistant Professor at the Mathematics Department of Gakushuin University in Japan. He obtained his Ph.D. from TU Munich under the supervision of Nina Gantert. Following his doctoral studies, he held postdoctoral positions at RIMS, Kyoto University, and Tsukuba University. Later, he worked as an Assistant Professor at AIMR, Tohoku University. Dr. Junk's research primarily focuses on probability theory and its applications to problems from mathematical physics and material science.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.