Density of eigenvalues of random normal matrices

Abstract

The relation between random normal matrices and conformal mappings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.

17 pages. Corrected version

References in corpus (4)

• Integrable Hierarchies and Dispersionless Limit
• Conformal maps and dispersionless integrable hierarchies
• Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
• On the structure of Normal Matrix Model

Cited by in corpus (37)

• Fluctuations of eigenvalues of random normal matrices
• Coulomb gas ensembles and Laplacian growth
• Random normal matrices and Ward identities
• Topology of quadrature domains
• A note on the second order universality at the edge of Coulomb gases on the plane
• The random normal matrix model: insertion of a point charge
• Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble
• Random normal matrices, Bergman kernel and projective embeddings
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Fine asymptotic behavior in eigenvalues of random normal matrices: Ellipse Case
• Quantum Hele-Shaw flow
• Universal hypotrochoidic law for random matrices with cyclic correlations
• A localization theorem for the planar Coulomb gas in an external field
• Painlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane
• The normal matrix model with a monomial potential, a vector equilibrium problem, and multiple orthogonal polynomials on a star
• Edge scaling limit of the spectral radius for random normal matrix ensembles at hard edge
• Dynamics of Schwarz reflections: the mating phenomena
• Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane
• Matrix-valued orthogonal polynomials related to hexagon tilings
• Growth of balls of holomorphic sections and energy at equilibrium
• Schwarz reflections and the Tricorn
• Density of Eigenvalues of Random Normal Matrices with an Arbitrary Potential, and of Generalized Normal Matrices
• Lemniscate ensembles with spectral singularity
• Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials
• Edge fluctuations for random normal matrix ensembles
• On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections
• Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling
• Orthogonal polynomials in the normal matrix model with two insertions
• Orthogonal polynomials in the normal matrix model with a cubic potential
• On the norms and roots of orthogonal polynomials in the plane and $L^p$-optimal polynomials with respect to varying weights
• Infinite-Dimensional Frobenius Manifolds for 2+1 Integrable Systems
• Integrability-preserving regularizations of Laplacian Growth
• Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation
• Edge behavior of two-dimensional Coulomb gases near a hard wall
• Universality for fluctuations of counting statistics of random normal matrices
• Large Deviations and Linear Statistics for Potential Theoretic Ensembles Associated with Regular Closed Sets
• Equilibrium measures for a class of potentials with discrete rotational symmetries