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

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.

arXiv comment60 pages, 3 figures; Version 2: Minor revisions

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Cited by in corpus (5)

• Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models
• Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles
• Tail estimates for the stationary stochastic six vertex model and ASEP
• Stationary measure for six-vertex model on a strip
• The stochastic six-vertex model speed process