Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlevé again.

Details Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlevé again. Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlevé again.

1995-03-15

arxiv.org/abs/cond-mat/9503077v1

Phys. Lett. A209 (1995) 173-178

Physics

Condensed Matter

9 pages, latex, no figures.

Scientific paper

10.1016/0375-9601(95)00834-6

The statistics of random band--matrices with width and strength of the band slowly varying along the diagonal is considered. The Dyson equation for the averaged Green function close to the edge of spectrum is reduced to the Painlev\'{e} I equation. The analytical properties of the Green function allow to fix the solution of this equation. The former appears to be the same as that arose within the random--matrix regularization of 2d-gravity.

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