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The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process
Chin Hang Lun, Jon Warren · 2016-06-16 · via math.PR updates on arXiv.org

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.

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