Eigenvalue density for a class of Jacobi matrices
Abstract
We obtain the asymptotic distribution of eigenvalues of real symmetric tridiagonal matrices as their dimension increases to infinity and whose diagonal and off-diagonal elements asymptotically change with the index n as Jnt+i nt+i aiφ(n), Jnt+i nt+i+1 biφ(n), i=0,1,...,t-1, where ai and bi are finite, and φ(n) belongs to a certain class of nondecreasing functions.
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