Berezin density and planar orthogonal polynomials

Random matrices (probabilistic aspects) (60B20) Asymptotic behavior of solutions to PDEs (35B40) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Asymptotic expansions of solutions to PDEs (35C20) Riemann-Hilbert problems in context of PDEs (35Q15)

Cites Work

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Orthogonal polynomials in the normal matrix model with a cubic potential
Fluctuations of eigenvalues of random normal matrices
On a set of polarized Kähler metrics on algebraic manifolds
A direct approach to Bergman kernel asymptotics for positive line bundles
The isomonodromy approach to matrix models in 2D quantum gravity
On bulk singularities in the random normal matrix model
Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane
Planar orthogonal polynomials and boundary universality in the random normal matrix model
Off-spectral analysis of Bergman kernels
Random normal matrices and Ward identities
A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane
Discontinuity in the asymptotic behavior of planar orthogonal polynomials under a perturbation of the Gaussian weight
Szegő type asymptotics for the reproducing kernel in spaces of full-plane weighted polynomials
Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane
Berezin transform in polynomial bergman spaces
An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation
Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
Coulomb gas ensembles and Laplacian growth
Spectral Approach to D‐bar Problems
Large-Nexpansion for the 2D Dyson gas
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
Soft Riemann‐Hilbert problems and planar orthogonal polynomials
Riemann-Hilbert hierarchies for hard edge planar orthogonal polynomials
A direct approach to the analytic Bergman projection

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