The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process
Probability
2016-06-17 v1
Abstract
We show that solutions of the stochastic heat equation driven by space-time white noise, although not smooth, meaningfully solve the two-dimensional Toda equations. Then by extending our arguments we show the time evolution of the multilayer process introduced by O'Connell and Warren is conjugate to a flow induced by the stochastic heat equation. In particular this establishes a Markov property conjectured by O'Connell and Warren. It also defines, for the first time, the multilayer process started from a general initial condition.
Keywords
Cite
@article{arxiv.1606.05139,
title = {The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process},
author = {Chin Hang Lun and Jon Warren},
journal= {arXiv preprint arXiv:1606.05139},
year = {2016}
}