Abstract

The theme of the talk is deriving stochastic PDE limits as description of large-scale fluctuations of the six-vertex (6V) model in various regimes.
We will consider two types of 6V model: stochastic 6V and symmetric 6V.
For stochastic 6V in a weakly asymmetric regime, under parabolic scaling the height function fluctuation converges to solution of KPZ equation after suitable re-centering and tilting. For symmetric 6V, in a regime where parameters are tuned into the ferroelectric/disordered phase critical point, under parabolic scaling the line density fluctuations in a one-parameter family of Gibbs states converge to solution of stationary stochastic Burgers.
Again for stochastic 6V, in a regime where the corner-shape vertex weights are tuned to zero, under hyperbolic scaling, the height fluctuation converges to the solution of stochastic telegraph equation.
We will discuss challenges and new techniques in the proofs.
Based on a joint work with Ivan Corwin, Promit Ghosal and Li-Cheng Tsai, and a joint work with Li-Cheng Tsai.