The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field
arXiv:math-ph/0506078 · doi:10.1007/s00220-008-0591-5
Abstract
In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.
68 pages. Smaller corrections: two inequalities in sections 3 and two inequalities in section 4, and definition of a Banach space in appendix A1. Presentation of LLN and CLT in section 4.3 improved. Notation improved
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Cited by in corpus (8)
- On the Dynamics of Large Particle Systems in the Mean Field Limit
- On Mean Field Limits for Dynamical Systems
- The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics
- Microscopic foundations of kinetic plasma theory: The relativistic Vlasov--Maxwell equations and their radiation-reaction-corrected generalization
- Combined Mean Field Limit and Non-relativistic Limit of Vlasov-Maxwell Particle System to Vlasov-Poisson System
- On the relativistic Vlasov-Poisson system
- A particle approximation for the relativistic Vlasov-Maxwell dynamics
- On the Joint Evolution Problem for a Scalar Field and its Singularity