Coulomb gas ensembles and Laplacian growth

Abstract

We consider the normal matrix ensemble under a general confining potential. We find that the eigenvalues condensate on a compact set in the plane, which we call the spectral droplet. We also study the evolution of incrementally adding a dimension, i.e., adding an extra electron in this fermionic model.

43 pages

References in corpus (3)

• Random normal matrices and Ward identities
• The polyanalytic Ginibre ensembles
• Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n

Cited by in corpus (36)

• Random normal matrices and Ward identities
• The polyanalytic Ginibre ensembles
• Topology of quadrature domains
• Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
• Random normal matrices, Bergman kernel and projective embeddings
• Fine asymptotic behavior in eigenvalues of random normal matrices: Ellipse Case
• A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
• Local density for two-dimensional one-component plasma
• Asymptotic expansion of polyanalytic Bergman kernels
• Discontinuity in the asymptotic behavior of planar orthogonal polynomials under a perturbation of the Gaussian weight
• The high temperature crossover for general 2D Coulomb gases
• A localization theorem for the planar Coulomb gas in an external field
• Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials
• Universality of the number variance in rotational invariant two-dimensional Coulomb gases
• Threshold condensation to singular support for a Riesz equilibrium problem
• 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
• Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges
• Dynamics of Schwarz reflections: the mating phenomena
• On boundary confinements for the Coulomb gas
• Quantitative stability of the free boundary in the obstacle problem
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Repulsion in low temperature $\beta$-ensembles
• Zeros of random polynomials and its higher derivatives
• Schwarz reflections and the Tricorn
• Off-spectral analysis of Bergman kernels
• Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling
• A note on normal matrix ensembles at the hard edge
• Orthogonal polynomials in the normal matrix model with two insertions
• Sharp deviation inequalities for the 2D Coulomb gas and Quantum hall states, I
• Microscopic densities and Fock-Sobolev spaces
• Edge behavior of two-dimensional Coulomb gases near a hard wall
• Universality for fluctuations of counting statistics of random normal matrices
• Bulk asymptotics for polyanalytic correlation kernels
• Equilibrium measures and partial balayage
• Large Deviations and Linear Statistics for Potential Theoretic Ensembles Associated with Regular Closed Sets