Journal of the Mathematical Society of Japan

Ginibre-type point processes and their asymptotic behavior

Tomoyuki SHIRAI

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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.

Article information

J. Math. Soc. Japan Volume 67, Number 2 (2015), 763-787.

First available in Project Euclid: 21 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60F05: Central limit and other weak theorems 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]

Ginibre point process determinantal point processes Landau Hamiltonian reproducing kernel Bargmann–Fock space Laguerre polynomial


SHIRAI, Tomoyuki. Ginibre-type point processes and their asymptotic behavior. J. Math. Soc. Japan 67 (2015), no. 2, 763--787. doi:10.2969/jmsj/06720763.

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