Large deviation theorem for zeros of polynomials and Hermitian random\n matrices

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

paper · pdf · doi:10.48550/arxiv.1611.04271

openalex publication_date 2016/11/14 · 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\nof zeros of polynomials and apply them to the characteristic polynomials of\nHermitian random matrices. We obtain new estimates related to the local\nsemi-circular law for the empirical spectral distribution of these matrices\nwhen the 4th moments of their entries are controlled.\n

Citations

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

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