A stochastic telegraph equation from the six-vertex model

A stochastic telegraph equation from the six-vertex model

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...

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Veröffentlicht in:arXiv.org 2019-04
Hauptverfasser: Borodin, Alexei, Gorin, Vadim
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Differential equations
Inhomogeneity
Variations
White noise
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description 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 corresponding law of large numbers -- the limit shape of the height function -- is described by the (deterministic) homogeneous telegraph equation.
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subjects Differential equations
Inhomogeneity
Variations
White noise
title A stochastic telegraph equation from the six-vertex model
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