The random normal matrix model: insertion of a point charge

DOI10.1007/s11118-021-09942-zOpenAlexW2799228354MaRDI QIDQ2684431

Yacin Ameur, Seong-Mi Seo, Nam-Gyu Kang

Publication date: 16 February 2023

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.08587

zbMATH Keywords

conical singularityFock-Sobolev spaceWard's equationmicroscopic limitplanar Coulomb gas

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Random matrices (algebraic aspects) (15B52) Statistical mechanics of plasmas (82D10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Statistical mechanics of gases (82D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (18)

Edge behavior of two-dimensional Coulomb gases near a hard wall ⋮ Wronskian structures of planar symplectic ensembles ⋮ Partial isometries, duality, and determinantal point processes ⋮ Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges ⋮ Determinantal Coulomb Gas Ensembles with a Class of Discrete Rotational Symmetric Potentials ⋮ The planar low temperature Coulomb gas: separation and equidistribution ⋮ Spherical induced ensembles with symplectic symmetry ⋮ Disk counting statistics near hard edges of random normal matrices: the multi-component regime ⋮ Law of large numbers for the maximum of the two-dimensional Coulomb gas potential ⋮ Large gap asymptotics on annuli in the random normal matrix model ⋮ Almost-Hermitian random matrices and bandlimited point processes ⋮ Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials ⋮ Exponential moments for disk counting statistics at the hard edge of random normal matrices ⋮ Random normal matrices in the almost-circular regime ⋮ Two-dimensional elliptic determinantal point processes and related systems ⋮ Scaling limits of random normal matrix processes at singular boundary points ⋮ Microscopic densities and Fock-Sobolev spaces ⋮ Exponential moments for disk counting statistics of random normal matrices in the critical regime

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional Brownian motion with Hurst index \({H = 0}\) and the Gaussian unitary ensemble
• On a problem for Ward's equation with a Mittag-Leffler potential
• Fluctuations of eigenvalues of random normal matrices
• On the structure of correlation functions in the normal matrix model
• On bulk singularities in the random normal matrix model
• The law of large numbers for the maximum of almost Gaussian log-correlated fields coming from random matrices
• Mesoscopic fluctuations for unitary invariant ensembles
• Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane
• Gaussian limit for determinantal random point fields.
• Near-boundary asymptotics for correlation kernels
• Two-dimensional elliptic determinantal point processes and related systems
• Scaling limits of random normal matrix processes at singular boundary points
• How much can the eigenvalues of a random Hermitian matrix fluctuate?
• Planar orthogonal polynomials and boundary universality in the random normal matrix model
• Maximum of the characteristic polynomial of the Ginibre ensemble
• Microscopic densities and Fock-Sobolev spaces
• Rescaling Ward identities in the random normal matrix model
• The high temperature crossover for general 2D Coulomb gases
• Random normal matrices and Ward identities
• On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials
• Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant
• Discontinuity in the asymptotic behavior of planar orthogonal polynomials under a perturbation of the Gaussian weight
• The supercritical regime in the normal matrix model with cubic potential
• Density of eigenvalues of random normal matrices
• The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem
• Topology of quadrature domains
• Gaussian free field and conformal field theory
• Characteristic Polynomials of Complex Random Matrices and Painlevé Transcendents
• The Mother Body Phase Transition in the Normal Matrix Model
• On the moments of the characteristic polynomial of a Ginibre random matrix
• Mittag-Leffler Functions, Related Topics and Applications
• Theory of Reproducing Kernels
• On the characteristic polynomial of a random unitary matrix

This page was built for publication: The random normal matrix model: insertion of a point charge