D. Kusnezov et Ch. Lewenkopf, LEVY DIFFUSION AND CLASSES OF UNIVERSAL PARAMETRIC CORRELATIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(3), 1996, pp. 2283-2286
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.