The sine kernel, two corresponding operator identities, and random matrices
Classical Analysis and ODEs
2021-06-07 v1 Functional Analysis
Probability
Spectral Theory
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2106.02389,
title = {The sine kernel, two corresponding operator identities, and random matrices},
author = {Lev Sakhnovich},
journal= {arXiv preprint arXiv:2106.02389},
year = {2021}
}
Comments
This paper is a prolongation (and an important development of some results) of our paper arXiv:2104.12694