Yuchen Liao: Lower tail large deviations for the stochastic six vertex model

Abstract:

 One characterizing feature of models in the KPZ universality class is the speed \(N\) vs \(N^2\) large deviations principle for the upper and lower tails of the random height functions. In this talk I will discuss a lower tail large deviations principle for the stochastic six vertex model (S6V) with step initial data. The approach is a combination of the following two ingredients:
1. An identity of Borodin-Olshanski connecting the randomly shifted S6V height functions to discrete orthogonal polynomial ensembles.
2. A probabilistic argument establishing weak log concavity of the height functions to get rid of the random shift.

Based on joint work with S. Das and M. Mucciconi.