The KMP heat transport process converges, in a t^{3/4} scaling window, to the multiplicative-noise stochastic heat equation (the exponential of KPZ) with noise coefficient 1/(2√α).
At the edge of a cloud of Brownian particles
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abstract
We study a simple model for the trajectory of a particle in a turbulent fluid, where a Brownian motion travels through a random Gaussian velocity field. We study the quenched law of the process and prove that in a weak environment setting, the fluctuations at the transition from weak to strong disorder are described by the KPZ equation. We conjecture the same is true without the assumption of a weak environment.
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Convergence of the KMP model to the KPZ equation
The KMP heat transport process converges, in a t^{3/4} scaling window, to the multiplicative-noise stochastic heat equation (the exponential of KPZ) with noise coefficient 1/(2√α).