A stochastic telegraph equation from the six-vertex model
Name
1803.09137.pdf
Description
Accepted version
Size
920.07 KB
Format
Adobe PDF
Checksum (MD5)
9a29c3a5bcb6c8122a3916bc56ebfb63
Author(s)
Borodin, Alexei
Gorin, Vadim
Date Issued
2019
Journal
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1214/19-AOP1356
