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Fluctuations of eigenvalues of random normal matrices

Ameur, Yacin and Hedenmalm, Håkan and Makarov, Nikolai (2011) Fluctuations of eigenvalues of random normal matrices. Duke Mathematical Journal, 159 (1). pp. 31-81. ISSN 0012-7094.

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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.

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Additional Information:© 2011 Duke University Press. Received 18 October 2009. Revision received 30 October 2010. Authors’ research supported by the Göran Gustafsson Foundation. Makarov’s work partially supported by National Science Foundation grant DMS-0201893. We are grateful to Alexei Borodin, Kurt Johansson, and Paul Wiegmann for help and useful discussions.
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Göran Gustafsson FoundationUNSPECIFIED
Issue or Number:1
Classification Code:2010 Mathematics Subject Classification: Primary 15B52; Secondary 82C22
Record Number:CaltechAUTHORS:20110808-135723507
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24744
Deposited By: Jason Perez
Deposited On:08 Aug 2011 22:42
Last Modified:03 Oct 2019 02:59

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