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A stochastic telegraph equation from the six-vertex model

Author(s)
Borodin, Alexei; Gorin, Vadim
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Abstract
© Institute of Mathematical Statistics, 2019. 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 twodimensional 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.
Date issued
2019
URI
https://hdl.handle.net/1721.1/133366
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
The Annals of Probability
Publisher
Institute of Mathematical Statistics

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