Microscopic densities and Fock-Sobolev spaces

We study two-dimensional eigenvalue ensembles close to certain types of singular points in the interior of the droplet. We prove existence of a microscopic density which quickly approaches the equilibrium density, as the distance from the singularity increases beyond the microscopic scale. This kind...

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Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 139; no. 1; pp. 397 - 420
Main Authors Ameur, Yacin, Seo, Seong-Mi
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.10.2019
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Analysis
Asymptotic properties
Density
Dynamical Systems and Ergodic Theory
Eigenvalues
Entire functions
Functional Analysis
Matematik
Matematisk analys
Mathematical Analysis
Mathematics
Mathematics and Statistics
Natural Sciences
Naturvetenskap
Partial Differential Equations
Sobolev space
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Summary:We study two-dimensional eigenvalue ensembles close to certain types of singular points in the interior of the droplet. We prove existence of a microscopic density which quickly approaches the equilibrium density, as the distance from the singularity increases beyond the microscopic scale. This kind of asymptotic is used to analyze normal matrix models in [3]. In addition, we obtain here asymptotics for the Bergman function of certain Fock-Sobolev spaces of entire functions.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-019-0055-1