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A quenched local limit theorem for stochastic flows
arxiv.org · saved by 1 readers
We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We impose no structural assumption (such as incompressibility) on the velocity field. We show that conditional on the velocity field, the quenched density of the particle after a long time can be approximated pointwise by the product of a deterministic Gaussian density and a spacetime-stationary random field.
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