A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality

DOI10.1007/s00023-020-00973-7zbMath1460.60004arXiv2004.07626OpenAlexW3017000404MaRDI QIDQ2662006

Sung-Soo Byun, Nam-Gyu Kang, Gernot Akemann

Publication date: 8 April 2021

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07626

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Linear algebraic groups over global fields and their integers (20G30) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (8)

Wronskian structures of planar symplectic ensembles ⋮ Determinantal Coulomb Gas Ensembles with a Class of Discrete Rotational Symmetric Potentials ⋮ Almost-Hermitian random matrices and bandlimited point processes ⋮ Universal scaling limits of the symplectic elliptic Ginibre ensemble ⋮ Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials ⋮ Unnamed Item ⋮ Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels ⋮ Scaling limits of planar symplectic ensembles

Uses Software

• DLMF

Cites Work

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• Products of independent non-Hermitian random matrices
• Fluctuations of eigenvalues of random normal matrices
• The complex Laguerre symplectic ensemble of non-Hermitian matrices
• Equilibrium measures for a class of potentials with discrete rotational symmetries
• Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics
• The circular law for random matrices
• The Ginibre ensemble of real random matrices and its scaling limits
• Quantum signatures of chaos. With a foreword by H. Haken
• On the structure of correlation functions in the normal matrix model
• Circular law
• Concentration for Coulomb gases and Coulomb transport inequalities
• Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble
• Large deviation principle for empirical fields of log and Riesz gases
• On bulk singularities in the random normal matrix model
• Random matrices: universality of ESDs and the circular law
• On fluctuations of eigenvalues of random Hermitian matrices.
• Scaling limits of random normal matrix processes at singular boundary points
• Rescaling Ward identities in the random normal matrix model
• Random normal matrices and Ward identities
• Edge scaling limits for a family of non-Hermitian random matrix ensembles
• Multi-critical unitary random matrix ensembles and the general Painlevé II equation
• Conformal and potential analysis in Hele-Shaw cells.
• Products of independent elliptic random matrices
• Dropping the independence: singular values for products of two coupled random matrices
• Topology of quadrature domains
• Fine asymptotic behavior for eigenvalues of random normal matrices: Ellipse case
• Gaussian free field and conformal field theory
• Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane
• Spectral analysis of stochastic recurrence systems of growing dimension under G-condition. Canonical equation K 91
• Universal microscopic correlation functions for products of independent Ginibre matrices
• Induced Ginibre ensemble of random matrices and quantum operations
• Universality of the double scaling limit in random matrix models
• Elliptic Law
• Double scaling limit in the random matrix model: The Riemann-Hilbert approach
• Coulomb gas ensembles and Laplacian growth
• Non-Hermitean Wishart random matrices (I)
• Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles
• Non-Hermitian extensions of Wishart random matrix ensembles
• Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)
• Large-Nexpansion for the 2D Dyson gas

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