A stochastic telegraph equation from the six-vertex model

Alexei Borodin; Vadim Gorin

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arXiv · 1803.09137

A stochastic telegraph equation from the six-vertex model

Alexei Borodin·Vadim Gorin

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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.

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BibTeX RIS

Alexei Borodin, Vadim Gorin. 2018-03-24. A stochastic telegraph equation from the six-vertex model. https://arxiv.org/abs/1803.09137

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