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

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 Painlevé 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.

preprint1995arXivOpen access
P. G. Silvestrov
cond-matchao-dynnlin.CDhep-th
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P. G. Silvestrov

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