About the stationary states of vortex systems

Thierry Bodineau; Alice Guionnet

doi:10.1016/S0246-0203(99)80011-9

About the stationary states of vortex systems

Thierry Bodineau
, Alice Guionnet

Laboratoire de Mathématiques d'Orsay

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the precise behaviour of a gas of vortices approximating the vorticity of an incompressible, inviscid, two dimensional fluid as proposed by Onsager [16]. For such mean field interacting particles system with positive vortices, the convergence of the empirical measure was proven in [3]. We improve this result by showing, for more general values of the vortices, that a large deviation principle holds. We also prove a central limit theorem for neutral gases.

Original language	English
Pages (from-to)	205-237
Number of pages	33
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	35
Issue number	2
DOIs	https://doi.org/10.1016/S0246-0203(99)80011-9
Publication status	Published - 1 Jan 1999
Externally published	Yes

Keywords

Central limit theorem
Interacting particle systems
Large deviations
Statistical mechanics of two-dimensional euler equations

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10.1016/S0246-0203(99)80011-9

Cite this

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AB - We investigate the precise behaviour of a gas of vortices approximating the vorticity of an incompressible, inviscid, two dimensional fluid as proposed by Onsager [16]. For such mean field interacting particles system with positive vortices, the convergence of the empirical measure was proven in [3]. We improve this result by showing, for more general values of the vortices, that a large deviation principle holds. We also prove a central limit theorem for neutral gases.

KW - Central limit theorem

KW - Interacting particle systems

KW - Large deviations

KW - Statistical mechanics of two-dimensional euler equations

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About the stationary states of vortex systems

Abstract

Keywords

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