Ginibre-type point processes and their asymptotic behavior

DOI10.2969/jmsj/06720763zbMath1319.60102OpenAlexW2077010388MaRDI QIDQ2351882

Tomoyuki Shirai

Publication date: 26 June 2015

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1429624603

zbMATH Keywords

Laguerre polynomialreproducing kernelBargmann-Fock spacedeterminantal point processesLandau HamiltonianGinibre point process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (20)

Husimi \(Q\)-functions attached to hyperbolic Landau levels ⋮ Partial isometries, duality, and determinantal point processes ⋮ Point processes, hole events, and large deviations: random complex zeros and Coulomb gases ⋮ The affine ensemble: determinantal point processes associated with the \(ax + b\) group ⋮ Harmonic analysis in phase space and finite Weyl-Heisenberg ensembles ⋮ The forbidden region for random zeros: Appearance of quadrature domains ⋮ Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble ⋮ Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles ⋮ Normality of smooth statistics for planar determinantal point processes ⋮ Exponential moments for disk counting statistics at the hard edge of random normal matrices ⋮ The Weyl–Heisenberg ensemble: hyperuniformity and higher Landau levels ⋮ Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator ⋮ Two-dimensional elliptic determinantal point processes and related systems ⋮ The hyperbolic-type point process ⋮ Generalized Wehrl entropies and Euclidean Landau levels ⋮ A set of \(q\)-coherent states for the Rogers-Szegő oscillator ⋮ A \(q\)-deformation of true-polyanalytic Bargmann transforms when \(q^{-1}>1\) ⋮ Local maxima of white noise spectrograms and Gaussian entire functions ⋮ Polyanalytic reproducing Kernels on the quantized annulus ⋮ Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes

Cites Work

• The polyanalytic Ginibre ensembles
• Overcrowding estimates for zeroes of planar and hyperbolic Gaussian analytic functions
• Determinantal processes and independence
• Random point fields associated with certain Fredholm determinants. I: Fermion, Poisson and Boson point processes.
• Gaussian limit for determinantal random point fields.
• Random complex zeroes. III: Decay of the hole probability
• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
• Large charge fluctuations in classical Coulomb systems
• Large deviations for the Fermion point process associated with the exponential kernel
• Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials
• On completeness of random exponentials in the Bargmann–Fock space
• Determinantal random point fields
• Asymptotics of the Hole Probability for Zeros of Random Entire Functions
• On a Hilbert space of analytic functions and an associated integral transform part I
• Bargmann representation for Landau levels in two dimensions
• Statistical Ensembles of Complex, Quaternion, and Real Matrices
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