Abstract
The determination of level-average properties (e.g. the level density) of physical systems often reduces to the calculation of spectral-average properties of the rational Jacobi matrices, i.e. Jacobi matrices whose elements are rational fractions of the suffix. Of special importance among these properties are the asymptotic ones, due to the infinite dimension of the Hilbert spaces associated with those systems. Here the author makes a detailed study of the asymptotical eigenvalue density of the rational Jacobi matrices by means of its moments. Compact expressions of these quantities in terms of the parameters which define the matrix elements are found analytically.
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