Dispersion of volume under the action of isotropic Brownian flows

Georgi Dimitroff; Michael Scheutzow

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arXiv · 0811.0276

Dispersion of volume under the action of isotropic Brownian flows

Georgi Dimitroff·Michael Scheutzow

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Abstract

We study transport properties of isotropic Brownian flows. Under a transience condition for the two-point motion, we show asymptotic normality of the image of a finite measure under the flow and -- under slightly stronger assumptions -- asymptotic normality of the distribution of the volume of the image of a set under the flow. Finally, we show that for a class of isotropic flows, the volume of the image of a nonempty open set (which is a martingale) converges to a random variable which is almost surely strictly positive.

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Georgi Dimitroff, Michael Scheutzow. 2008-11-03. Dispersion of volume under the action of isotropic Brownian flows. https://arxiv.org/abs/0811.0276

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