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spectrum of a symmetric tridiagonal random matrix
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pf.buonsante@gmail.com
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Joined: 19 Jul 2006
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PostPosted: Wed Jul 19, 2006 9:45 am    Post subject: spectrum of a symmetric tridiagonal random matrix Reply with quote

Hi everybody,

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

Francesco
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