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April, 2015 Ginibre-type point processes and their asymptotic behavior
Tomoyuki SHIRAI
J. Math. Soc. Japan 67(2): 763-787 (April, 2015). DOI: 10.2969/jmsj/06720763


We introduce Ginibre-type point processes as determinantal point processes associated with the eigenspaces corresponding to the so-called Landau levels. The Ginibre point process, originally defined as the limiting point process of eigenvalues of the Ginibre complex Gaussian random matrix, can be understood as a special case of Ginibre-type point processes. For these point processes, we investigate the asymptotic behavior of the variance of the number of points inside a growing disk. We also investigate the asymptotic behavior of the conditional expectation of the number of points inside an annulus given that there are no points inside another annulus.


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Tomoyuki SHIRAI. "Ginibre-type point processes and their asymptotic behavior." J. Math. Soc. Japan 67 (2) 763 - 787, April, 2015.


Published: April, 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1319.60102
MathSciNet: MR3340195
Digital Object Identifier: 10.2969/jmsj/06720763

Primary: 60G55
Secondary: 46E22 , 60F05

Keywords: Bargmann–Fock space , Determinantal point processes , Ginibre point process , Laguerre polynomial , Landau Hamiltonian , reproducing kernel

Rights: Copyright © 2015 Mathematical Society of Japan


Vol.67 • No. 2 • April, 2015
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