A stochastic telegraph equation from the six-vertex model
Probability
2019-04-10 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1803.09137,
title = {A stochastic telegraph equation from the six-vertex model},
author = {Alexei Borodin and Vadim Gorin},
journal= {arXiv preprint arXiv:1803.09137},
year = {2019}
}
Comments
63 pages. v3: Conjecture 6.1 is now Theorem 6.1. To appear in Annals of Probability