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.
Citation
Alexei Borodin. Vadim Gorin. "A stochastic telegraph equation from the six-vertex model." Ann. Probab. 47 (6) 4137 - 4194, November 2019. https://doi.org/10.1214/19-AOP1356
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