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

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

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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

Information

Received: 1 July 2018; Revised: 1 February 2019; Published: November 2019
First available in Project Euclid: 2 December 2019

zbMATH: 07212180
MathSciNet: MR4038051
Digital Object Identifier: 10.1214/19-AOP1356

Subjects:
Primary: 35R60, 60G60, 60H15, 82B20

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • November 2019
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