Large Deviation Theorem for Zeros of Polynomials and Hermitian Random Matrices

Large Deviation Theorem for Zeros of Polynomials and Hermitian Random Matrices

We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of Hermitian random matrices. We obtain new estimates related to the local semi-circular law for the empirical spectral distribution of these matrice...

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Veröffentlicht in:The Journal of Geometric Analysis 2020-07, Vol.30 (3), p.2558-2580
1. Verfasser: Dinh, Tien-Cuong
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Deviation
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Gennadi Henkin: In Memoriam
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Polynomials
Theorems
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Beschreibung
Zusammenfassung:We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of Hermitian random matrices. We obtain new estimates related to the local semi-circular law for the empirical spectral distribution of these matrices when the 4th moments of their entries are controlled.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-017-9951-8