# Stochastic PDE Limit of the Six Vertex Model

@article{Corwin2020StochasticPL, title={Stochastic PDE Limit of the Six Vertex Model}, author={Ivan Corwin and Promit Ghosal and Hao Shen and Li-Cheng Tsai}, journal={Communications in Mathematical Physics}, year={2020}, volume={375}, pages={1945-2038} }

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $$\Delta \rightarrow 1^+$$ Δ → 1 + so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge to the solution to the Kardar–Parisi–Zhang (KPZ) equation. We also prove that the one-dimensional family of stochastic Gibbs states for the symmetric six vertex model converge under the same scaling to the stationary solution to the…

## 37 Citations

### Irreversible Markov Dynamics and Hydrodynamics for KPZ States in the Stochastic Six Vertex Model

- Mathematics
- 2022

We introduce a family of Markov growth processes on discrete height functions defined on the 2-dimensional square lattice. Each height function corresponds to a configuration of the six vertex model…

### Two-point convergence of the stochastic six-vertex model to the Airy process

- Mathematics
- 2020

In this paper we consider the stochastic six-vertex model in the quadrant started with step initial data. After a long time $T$, it is known that the one-point height function fluctuations are of…

### The KPZ Equation, Non-Stationary Solutions, and Weak Universality for Finite-Range Interactions

- Mathematics
- 2018

We study the weak KPZ universality problem by extending the KPZ universality results for weakly asymmetric exclusion processes to non-simple variants under deterministic initial data with constant…

### Shift‐invariance for vertex models and polymers

- MathematicsProceedings of the London Mathematical Society
- 2022

We establish a symmetry in a variety of integrable stochastic systems: certain multi‐point distributions of natural observables are unchanged under a shift of a subset of observation points. The…

### Time evolution of the Kardar-Parisi-Zhang equation

- Mathematics
- 2020

The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The…

### Coloured stochastic vertex models and their spectral theory

- Mathematics
- 2018

This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following: …

### Nonexistence and uniqueness for pure states of ferroelectric six‐vertex models

- MathematicsProceedings of the London Mathematical Society
- 2022

In this paper, we consider the existence and uniqueness of pure states with some fixed slope (s,t)∈[0,1]2$(s, t) \in [0, 1]^2$ for a general ferroelectric six‐vertex model. First, we show there is an…

### A stochastic telegraph equation from the six-vertex model

- MathematicsThe Annals of Probability
- 2019

A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are…

### Dualities in quantum integrable many-body systems and integrable probabilities. Part I

- MathematicsJournal of High Energy Physics
- 2022

Abstract
In this study we map the dualities observed in the framework of integrable probabilities into the dualities familiar in a realm of integrable many-body systems. The dualities between the…

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