00 1 Limit Distributions of Many – Particle Spectra Piotr

We find the limit distributions for a spectrum of a system of n particles governed by a k–body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q–deformed Gaussian distribution with the deformation parameter q depending on the value of the fraction k √ n . The family of q–deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig1, Wig2], Mon and French [MF]. PACS: 05.40.+j