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arXiv · 1902.10867

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

Amol Aggarwal
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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 in 1992 and by Reshetikhin-Sridhar in 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.

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BibTeXRIS

Amol Aggarwal. 2019-02-28. Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model. https://doi.org/10.1007/s00220-019-03643-w

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