Abstract
We consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the canonical Gibbs ensemble at inverse temperature . We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when a generalized version of two-dimensional Euler dynamics preserving the Gaussian energy-enstrophy ensemble.
Funding Statement
The third author acknowledges the partial support of the project PNRR—M4C2—Investimento 1.3, Partenariato Esteso PE00000013—FAIR—Future Artificial Intelligence Research—Spoke 1 Human-centered AI, funded by the European Commission under the NextGeneration EU programme, of the project Noise in fluid dynamics and related models funded by the MUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2022—grant 20222YRYSP, of the project APRISE—Analysis and Probability in Science funded by the the University of Pisa, grant PRA_2022_85, and of the MUR Excellence Department Project awarded to the Department of Mathematics, University of Pisa, CUP I57G22000700001.
Acknowledgments
The first author wishes to thank Alessandro Iraci for insightful remarks on the combinatorial arguments in Section 3.
Citation
Francesco Grotto. Eliseo Luongo. Marco Romito. "Gibbs equilibrium fluctuations of point vortex dynamics." Ann. Appl. Probab. 34 (6) 5426 - 5461, December 2024. https://doi.org/10.1214/24-AAP2095
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