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

  • Amol AggarwalEmail author


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.



The author heartily thanks Alexei Borodin, Ivan Corwin, and Jeffrey Kuan for enlightening discussions. The author is also grateful to the anonymous referee for helpful suggestions on an earlier draft of this manuscript. This work was partially supported by the NSF Graduate Research Fellowship under Grant Number DGE1144152 and NSF Grant DMS-1664619.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeUSA

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