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

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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… Click to show full abstract

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 shape are given by an infinite-volume, translation-invariant Gibbs measure of the appropriate slope.

Keywords: vertex model; limit; stochastic six; six vertex; local statistics

Journal Title: Communications in Mathematical Physics
Year Published: 2019

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