A stochastic telegraph equation from the six-vertex model

2018/03/24 by Borodin, Alexei, Gorin, Vadim · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1803.09137

Abstract

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.

Cited by

• Explicit correlation functions for the six-vertex model in the free-fermion regime
• Metastability for telegraph processes in a double-well potential

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