Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 17 (2012), paper no. 19, 12 pp.
A note on large deviations for 2D Coulomb gas with weakly confining potential
We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence the empirical measure is seen to converge towards a non-random limiting measure, characterized by a variational principle from logarithmic potential theory, which may not have compact support. The proof of the large deviation upper bound is based on a compactification procedure which may be of help for further large deviation principles.
Electron. Commun. Probab. Volume 17 (2012), paper no. 19, 12 pp.
Accepted: 17 May 2012
First available in Project Euclid: 7 June 2016
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Hardy, Adrien. A note on large deviations for 2D Coulomb gas with weakly confining potential. Electron. Commun. Probab. 17 (2012), paper no. 19, 12 pp. doi:10.1214/ECP.v17-1818. https://projecteuclid.org/euclid.ecp/1465263152.