Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model

  title={Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model},
  author={Amol Aggarwal},
  journal={Communications in Mathematical Physics},
  • A. Aggarwal
  • Published 28 February 2019
  • Mathematics
  • Communications in Mathematical Physics
In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by the entropy solution to an explicit, non-linear conservation law that was predicted by Gwa–Spohn (Phys Rev Lett 68:725–728, 1992) and by Reshetikhin–Sridhar (Commun Math Phys 363:741–765, 2018). Then, we show that the local statistics of this model around any continuity point of its limit… 

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