Stochastic PDE Limit of the Six Vertex Model

  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},
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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