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At the edge of a cloud of Brownian particles

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arxiv 2208.11952 v1 pith:2VJQTLPI submitted 2022-08-25 math.PR

Dom Brockington , Jon Warren This is my paper · ORCID
classification math.PR
keywords weakbrownianenvironmentassumptioncloudconjecturedescribeddisorder
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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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  1. Convergence of the KMP model to the KPZ equation

    math.PR 2025-07 conditional novelty 7.0 of 10

    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).

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