Gibbs Equilibrium Fluctuations of Point Vortex Dynamics
- Authors: Francesco Grotto, Eliseo Luongo, Marco Romito
- Preprint year: 2023
- First public date: 2023-07-31
- arXiv: 2308.00163
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Annals of Applied Probability (2024)
- DOI: 10.1214/24-AAP2095
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 $\beta\geq 0$. We prove that the space-time fluctuation field around the (constant) Mean Field limit satisfies when $N\to\infty$ a generalized version of 2-dimensional Euler dynamics preserving the Gaussian Energy-Enstrophy ensemble.