Duke Mathematical Journal

Fluctuations of eigenvalues of random normal matrices

Yacin Ameur, Håkan Hedenmalm, and Nikolai Makarov

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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.

Article information

Duke Math. J., Volume 159, Number 1 (2011), 31-81.

First available in Project Euclid: 11 July 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15B52: Random matrices
Secondary: 82C22: Interacting particle systems [See also 60K35]


Ameur, Yacin; Hedenmalm, Håkan; Makarov, Nikolai. Fluctuations of eigenvalues of random normal matrices. Duke Math. J. 159 (2011), no. 1, 31--81. doi:10.1215/00127094-1384782. https://projecteuclid.org/euclid.dmj/1310416362

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