# A stochastic telegraph equation from the six-vertex model

@article{Borodin2019AST, title={A stochastic telegraph equation from the six-vertex model}, author={Alexei Borodin and Vadim Gorin}, journal={The Annals of Probability}, year={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 proportional to the two-dimensional white noise, and solutions to our equation are two-dimensional random Gaussian fields. We show that such fields arise naturally as asymptotic fluctuations of the height function in a certain limit regime of the stochastic six vertex model in a quadrant. The…

## 15 Citations

The stochastic telegraph equation limit of the stochastic higher spin six vertex model

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In this paper, we prove that the stochastic telegraph equation arises as a scaling limit of the stochastic higher spin six vertex (SHS6V) model with general spin $I/2, J/2$. This extends results of…

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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…

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In this article we study the stochastic six vertex model under the scaling proposed by Borodin and Gorin (2018), where the weights of corner-shape vertices are tuned to zero, and prove Conjecture 6.1…

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We study the stochastic colored six vertex (SC6V) model and its fusion. Our main result is an integral expression for natural observables of this model -- joint q-moments of height functions. This…

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. In this paper, we study the stationary distribution for the stochastic vertex models. Our main focus is the stochastic six vertex (S6V) model. We show that the extreme stationary distributions of…

KPZ Equation Limit of Stochastic Higher Spin Six Vertex Model

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We consider the stochastic higher spin six vertex (SHS6V) model introduced in [Corwin-Petrov, 2016] with general integer spin parameters $I, J$. Starting from near stationary initial condition, we…

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