The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. This includes the disordered pinning model with tail exponent 1/2, the usual (short-range) directed polymer model in dimension two, and the long-range directed polymer model with Cauchy tails in dimension one. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field with a multi-scale correlation structure, which undergoes a phase transition as the disorder strength varies. As a by-product, we show that the solution of the two-dimensional Stochastic Heat Equation, suitably regularized, converges to the same limit. Joint work with F. Caravenna and N. Zygouras.
Rongfeng Sun obtained his Ph.D. from New York University in 2004. He was a postdoc in EURANDOM, TU Eindhoven, from 2004-2006, and a postdoc in TU Berlin from 2006-2008. He then joined the National University of Singapore, where he is currently an associate professor. His research interests are in probability theory, and in particular, in interacting particle systems and models from statistical mechanics.