Large deviation theorem for zeros of polynomials and Hermitian random matrices

2016/11/14 by Tien‐Cuong Dinh, Tien-Cuong Dinh, Dinh, Tien-Cuong · 1 citation
Mathematics · #12B52 #60B20 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Random Matrices and Applications #math.CV #math.PR #msc:12B52 #msc:60B20

paper · pdf · doi:10.48550/arxiv.1611.04271

19 pages

arxiv created 2016/11/14 · openalex publication_date 2016/11/14 · arxiv updated 2016/11/15 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Random matrices: Universality of local eigenvalue statistics
• On the Distribution of the Roots of Certain Symmetric Matrices

Cited by

• A survey on asymptotic equilibrium distribution of zeros of random holomorphic sections

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