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Limit Theorems and Fluctuations for Point Vortices of Generalized Euler Equations

Geldhauser, Carina LU orcid and Romito, Marco (2021) In Journal of Statistical Physics 182(3).
Abstract

We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Central limit theorem, Generalized SQG, Law of large numbers, Mean field limit, Point vortices
in
Journal of Statistical Physics
volume
182
issue
3
article number
60
publisher
Springer
external identifiers
  • scopus:85102476458
ISSN
0022-4715
DOI
10.1007/s10955-021-02737-x
language
English
LU publication?
yes
id
424c0e7f-6e98-4af9-a2b2-6229de44e175
date added to LUP
2021-03-24 13:43:42
date last changed
2025-04-04 13:57:04
@article{424c0e7f-6e98-4af9-a2b2-6229de44e175,
  abstract     = {{<p>We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.</p>}},
  author       = {{Geldhauser, Carina and Romito, Marco}},
  issn         = {{0022-4715}},
  keywords     = {{Central limit theorem; Generalized SQG; Law of large numbers; Mean field limit; Point vortices}},
  language     = {{eng}},
  number       = {{3}},
  publisher    = {{Springer}},
  series       = {{Journal of Statistical Physics}},
  title        = {{Limit Theorems and Fluctuations for Point Vortices of Generalized Euler Equations}},
  url          = {{http://dx.doi.org/10.1007/s10955-021-02737-x}},
  doi          = {{10.1007/s10955-021-02737-x}},
  volume       = {{182}},
  year         = {{2021}},
}