# Stochastic PDE Limit of the Six Vertex Model

@article{Corwin2020StochasticPL,
title={Stochastic PDE Limit of the Six Vertex Model},
author={Ivan Corwin and Promit Ghosal and Hao Shen and Li-Cheng Tsai},
journal={Communications in Mathematical Physics},
year={2020},
volume={375},
pages={1945-2038}
}
• Published 21 March 2018
• Mathematics
• Communications in Mathematical Physics
We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $$\Delta \rightarrow 1^+$$ Δ → 1 + so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge to the solution to the Kardar–Parisi–Zhang (KPZ) equation. We also prove that the one-dimensional family of stochastic Gibbs states for the symmetric six vertex model converge under the same scaling to the stationary solution to the…

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