Asymptotics of the Eigenvalues of Two-Diagonal Jacobi Matrices

TL;DR

This paper analyzes the asymptotic behavior of eigenvalues for a specific class of Jacobi matrices with zero main diagonal and off-diagonal coefficients tending to zero, providing insights into their spectral properties.

Contribution

It derives the asymptotic formulas for eigenvalues of these Jacobi matrices, extending understanding of their spectral characteristics.

Findings

Eigenvalues follow specific asymptotic distributions.

The off-diagonal decay influences eigenvalue asymptotics.

Results apply to matrices with zero main diagonal and diminishing off-diagonals.

Abstract

We compute the asymptotics of eigenvalues of Jacobi matrices with the zero coefficients on the main diagonal and the off-diagonal coefficients which converge to zero.