Eigenvalue density for a class of Jacobi matrices
Abstract
Description
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 J_{nt+i nt+i}\sim a_iϕ(n), J_{nt+i nt+i+1}\sim b_iϕ(n), i=0,1,...,t-1, where a_i and b_i are finite, and ϕ(n) belongs to a certain class of nondecreasing functions.
9 pages including 2 postscript figures, Latex
9 pages including 2 postscript figures, Latex