We investigate a Coulomb gas in a potential satisfying a weaker growthView original: http://arxiv.org/abs/1202.2809
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.