A STOCHASTIC TELEGRAPH EQUATION FROM THE SIX-VERTEX MODEL

• 成果类型: Article
• 署名作者: Borodin, Alexei; Gorin, Vadim
• 署名单位: Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1356
• 发表日期: 2019
• 页码: 4137-4194
• 关键词: nonlinear-wave-equations; limit shapes; driven; smoothness; EXISTENCE; burgers; noise; asep

摘要

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.