LEVY DIFFUSION AND CLASSES OF UNIVERSAL PARAMETRIC CORRELATIONS

A general formulation of translationally invariant, parametrically cor related random matrix ensembles is used to classify universality in co rrelation functions. Surprisingly, the range of possible physical syst ems is bounded and can be labeled by a parameter alpha epsilon (0, 2), in a manner analogous to Levy diffusion. Universality is obtained aft er scaling by the (anomalous) diffusion constant D-alpha (the usual sc aling is divergent for alpha < 2). For each alpha, correlation functio ns are universal and distinct. The previous results in the literature correspond to the limiting case of superdiffusion alpha = 2.