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arXiv · 1207.2233

Gaussian convergence for stochastic acceleration of $\cN$ particles in the dense spectrum limit

Yves Elskens
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Abstract

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant modulo $π/2$ and the power spectrum expectation is uniform. The proof provides a full probabilistic foundation to the quasilinear approximation in this limit. The result extends to an arbitrary number of particles, founding the use of the ensemble picture for their behaviour in a single realization of the stochastic wave field.

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Yves Elskens. 2012-07-10. Gaussian convergence for stochastic acceleration of $\cN$ particles in the dense spectrum limit. https://arxiv.org/abs/1207.2233

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