Fluctuations of eigenvalues of random normal matrices
Yacin Ameur, Håkan Hedenmalm, and Nikolai Makarov
Source: Duke Math. J. Volume 159, Number 1
(2011), 31-81.
Abstract
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.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1310416362
Digital Object Identifier: doi:10.1215/00127094-1384782
Zentralblatt MATH identifier: 05941081
Mathematical Reviews number (MathSciNet): MR2817648
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