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.
"A note on large deviations for 2D Coulomb gas with weakly confining potential." Electron. Commun. Probab. 17 1 - 12, 2012. https://doi.org/10.1214/ECP.v17-1818