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May 2015 Random normal matrices and Ward identities
Yacin Ameur, Haakan Hedenmalm, Nikolai Makarov
Ann. Probab. 43(3): 1157-1201 (May 2015). DOI: 10.1214/13-AOP885


We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman’s solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of the fluctuations, and we show that the potential field of the corrected fluctuations converge on smooth test functions to a Gaussian free field with free boundary conditions on the droplet associated with the potential.


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Yacin Ameur. Haakan Hedenmalm. Nikolai Makarov. "Random normal matrices and Ward identities." Ann. Probab. 43 (3) 1157 - 1201, May 2015.


Published: May 2015
First available in Project Euclid: 5 May 2015

zbMATH: 06455731
MathSciNet: MR3342661
Digital Object Identifier: 10.1214/13-AOP885

Primary: 15B52 , 46E22 , 60B20

Keywords: Eigenvalues , Gaussian free field , Ginibre ensemble , loop equation , Random normal matrix , Ward identity

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 3 • May 2015
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