The sine kernel, two corresponding operator identities, and random matrices

2021/06/04 by Lev Sakhnovich, Sakhnovich, Lev
Mathematics · #34A30 #45B05 #60G99 #Advanced Algebra and Geometry #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Random Matrices and Applications #Spectral Theory (math.SP) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2106.02389

openalex publication_date 2021/06/04 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

Abstract

In the present paper, we consider the integral operator, which acts in Hilbert space and has sine kernel. This operator generates two operator identities and two corresponding canonical differential systems. We find the asymptotics of the corresponding resolvent and Hamiltonians. We use both the method of operator identities and the theory of random matrices.

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