Gaussian convergence for stochastic acceleration of $\cN$ particles in the dense spectrum limit
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 $\pi/2$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2012
- DOI:
- 10.48550/arXiv.1207.2233
- arXiv:
- arXiv:1207.2233
- Bibcode:
- 2012arXiv1207.2233E
- Keywords:
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- Mathematical Physics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 19 pp