science forum beginner
Joined: 19 Jul 2006
|Posted: Wed Jul 19, 2006 9:45 am Post subject:
spectrum of a symmetric tridiagonal random matrix
I am interested in the spectral features of an apparently simple class
of random matrices.
These matrices are real, symmetric and non-negative. The only non-zero
entries are those on the diagonals adjacent to the principal diagonal.
In summary, I am dealing with a one-dimensional random-hopping model,
or off-diagonal Anderson model.
The problem looks very "basic", and I have the feeling that many of its
properties can be (and probably have been) investigated analytically,
at least when the matrix elements are "simply" random.
I am particularly interested in the spectral radius for these matrices,
and in the behaviour (divergent or non-divergent) of the integrated
spectral density in the vicinity of the largest eigenvalue.
Are there analytic results? I am doing extensive bibliographic
researches, but so far I have found mostly numeric investigations.
Thanks a lot