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

## TL;DR

This paper analyzes the stochastic six-vertex model on a cylinder, demonstrating the emergence of a limit shape governed by a conservation law and characterizing local statistics through Gibbs measures.

## Contribution

It establishes the existence of a limit shape and describes local statistics using Gibbs measures, confirming long-standing predictions for the model.

## Key findings

- Limit shape described by a non-linear conservation law
- Local statistics given by translation-invariant Gibbs measures
- Validation of predictions by Gwa-Spohn and Reshetikhin-Sridhar

## 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.