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Shirai, Tomoyuki

Ginibre-type point processes and their asymptotic behavior. (English) Zbl 1319.60102

J. Math. Soc. Japan 67, No. 2, 763-787 (2015).
Summary: 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.

Cited in 11 Documents

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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)

Keywords:

Ginibre point process; determinantal point processes; Landau Hamiltonian; reproducing kernel; Bargmann-Fock space; Laguerre polynomial
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\textit{T. Shirai}, J. Math. Soc. Japan 67, No. 2, 763--787 (2015; Zbl 1319.60102)
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