Directed polymer models are well known Gibbs measures on random walk paths. Canonically they are defined so as to tilt the path distribution towards regions of space-time where an independent random field happens to be large, and as a result the paths tend to exhibit superdiffusive Kardar-Parisi-Zhang type fluctuation exponents, somehow betraying their random walk upbringing. Constructing these models on in the discrete space-time setting with a finite time horizon is straightforward, but extending them to infinite time horizons is difficult even in the fully discrete setting. I will review some relatively recent progress in the discrete and semi-discrete setting by myself and several other authors, some previous work of myself, Khanin, and Quastel on constructing continuous space-time models in the finite time horizon setting, and some attempts in progress to connect the two.

Date

May 31, 2019 16:00 +0800 — 17:30 +0800

Event

Location

Korean Institute of Advanced Study

85 Hoegiro Dongdaemun-gu, Seoul, Seoul 1325