In this article, we consider a fairly general potential in the plane and the corresponding Boltzmann-Gibbs distribution of eigenvalues of random normal matrices. As the order of the matrices tends to infinity, the eigenvalues condensate on a certain compact subset of the plane-the "droplet." We prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a Gaussian field, and we discuss various ramifications of this result.
NATURVETENSKAP -- Matematik (hsv//swe)
NATURAL SCIENCES -- Mathematics (hsv//eng)
NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)