Microscopic densities and Fock-Sobolev spaces

Abstract

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.

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Correspondence to Yacin Ameur.

Additional information

Seo was supported by Samsung Science and Technology Foundation, SSTF-BA1401-01.

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Ameur, Y., Seo, SM. Microscopic densities and Fock-Sobolev spaces. JAMA 139, 397–420 (2019). https://doi.org/10.1007/s11854-019-0055-1

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