## Duke Mathematical Journal

### Fluctuations of eigenvalues of random normal matrices

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 11 July 2011

https://projecteuclid.org/euclid.dmj/1310416362

Digital Object Identifier
doi:10.1215/00127094-1384782

Mathematical Reviews number (MathSciNet)
MR2817648

Zentralblatt MATH identifier
1225.15030

Subjects
Primary: 15B52: Random matrices

#### Citation

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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