The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process

The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process

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 conjuga...

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Veröffentlicht in:arXiv.org 2016-06
Hauptverfasser: Chin, Hang Lun, Warren, Jon
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Markov processes
Mathematical analysis
Multilayers
Thermodynamics
White noise
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description 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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subjects Markov processes
Mathematical analysis
Multilayers
Thermodynamics
White noise
title The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process
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