Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 12, 18 pp.
Concentration for Coulomb gases on compact manifolds
We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle system by using an empirical measure. Our main result is a concentration inequality in Kantorovich-Wasserstein distance inspired from the work of Chafaï, Hardy and Maïda on the Euclidean space. Their proof involves large deviation techniques together with an energy-distance comparison and a regularization procedure based on the superharmonicity of the Green function. This last ingredient is not available on a manifold. We solve this problem by using the heat kernel and its short-time asymptotic behavior.
Electron. Commun. Probab., Volume 24 (2019), paper no. 12, 18 pp.
Received: 12 September 2018
Accepted: 16 January 2019
First available in Project Euclid: 21 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
García-Zelada, David. Concentration for Coulomb gases on compact manifolds. Electron. Commun. Probab. 24 (2019), paper no. 12, 18 pp. doi:10.1214/19-ECP211. https://projecteuclid.org/euclid.ecp/1553133701