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

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.

This paper is a prolongation (and an important development of some results) of our paper arXiv:2104.12694