GAUSSIAN ENSEMBLE OF TRIDIAGONAL SYMMETRICAL RANDOM MATRICES

We obtained exact energy level correlators for the Gaussian ensemble o f finite tridiagonal symmetric matrices by employing the connection be tween the linear eigenvalue problem and periodic Toda equations. Solut ions of the latter help us to parametrise matrices in the ensemble, wh ich is equivalent to the decomposition onto the spectral and rotationa l degrees of freedom in the theory of filled random matrices. The rota tional variables can be integrated out reducing expressions for energy level correlators to multidimensional integrals over eigenvalues only , We found that density of states for the considered ensemble does not have a semicircle shape as N --> infinity. The spectral statistics ap proaches the Poisson type with one singular point in the same limit. ( C) 1997 Elsevier Science B.V.