Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels

DOI10.1007/s00220-021-04230-8zbMath1503.33008arXiv2103.12114OpenAlexW3209566505MaRDI QIDQ2070869

Gernot Akemann, Markus Ebke, Iván Parra

Publication date: 24 January 2022

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.12114

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Kernel functions in one complex variable and applications (30C40)

Related Items (8)

Wronskian structures of planar symplectic ensembles ⋮ On the almost‐circular symplectic induced Ginibre ensemble ⋮ Spherical induced ensembles with symplectic symmetry ⋮ Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble ⋮ Universal scaling limits of the symplectic elliptic Ginibre ensemble ⋮ Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials ⋮ Scaling limits of planar symplectic ensembles ⋮ Universality of the number variance in rotational invariant two-dimensional Coulomb gases

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The complex Laguerre symplectic ensemble of non-Hermitian matrices
• Massive partition functions and complex eigenvalue correlations in matrix models with symplectic symmetry
• New orthogonality relations for the Hermite polynomials and related Hilbert spaces
• The Ginibre ensemble of real random matrices and its scaling limits
• The probability that a random real Gaussian matrix has \(k\) real eigenvalues, related distributions, and the circular law
• Characteristic polynomials of complex random matrix models
• Classical skew orthogonal polynomials and random matrices
• Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
• Scaling limits of random normal matrix processes at singular boundary points
• Gegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane
• A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
• LAUGHLIN'S WAVE FUNCTIONS, COULOMB GASES AND EXPANSIONS OF THE DISCRIMINANT
• Skew orthogonal polynomials for the real and quaternion real Ginibre ensembles and generalizations
• Products of independent quaternion Ginibre matrices and their correlation functions
• RANDOM RIGHT EIGENVALUES OF GAUSSIAN QUATERNIONIC MATRICES
• Non-Hermitian Random Matrix Ensembles
• Universal microscopic correlation functions for products of independent Ginibre matrices
• Induced Ginibre ensemble of random matrices and quantum operations
• On a Hilbert space of analytic functions and an associated integral transform part I
• Generalized Fock Spaces and Associated Operators
• Distribution of complex eigenvalues for symplectic ensembles of non-Hermitian matrices
• A limit theorem at the edge of a non-Hermitian random matrix ensemble
• Eigenvalue correlations in non-Hermitean symplectic random matrices
• Eigenvalue statistics of random real matrices
• Truncations of random unitary matrices
• Products and ratios of characteristic polynomials of random Hermitian matrices
• Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
• Coherence, Squeezing and Entanglement: An Example of Peaceful Coexistence
• Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem
• The chiral Gaussian two-matrix ensemble of real asymmetric matrices
• Statistical Ensembles of Complex, Quaternion, and Real Matrices
• The Random Matrix Theory of the Classical Compact Groups
• Quantum signatures of chaos

This page was built for publication: Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels