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15 July 2011 Fluctuations of eigenvalues of random normal matrices
Yacin Ameur, Håkan Hedenmalm, Nikolai Makarov
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Duke Math. J. 159(1): 31-81 (15 July 2011). DOI: 10.1215/00127094-1384782

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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Yacin Ameur. Håkan Hedenmalm. Nikolai Makarov. "Fluctuations of eigenvalues of random normal matrices." Duke Math. J. 159 (1) 31 - 81, 15 July 2011. https://doi.org/10.1215/00127094-1384782

Information

Published: 15 July 2011
First available in Project Euclid: 11 July 2011

zbMATH: 1225.15030
MathSciNet: MR2817648
Digital Object Identifier: 10.1215/00127094-1384782

Subjects:
Primary: 15B52
Secondary: 82C22

Rights: Copyright © 2011 Duke University Press

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Vol.159 • No. 1 • 15 July 2011
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