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 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].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-32,
author = {Piotr \'Sniady},
title = {Limit distributions of many-particle spectra and q-deformed Gaussian variables},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {409-414},
zbl = {1134.81426},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-32}
}
Piotr Śniady. Limit distributions of many-particle spectra and q-deformed Gaussian variables. Banach Center Publications, Tome 72 (2006) pp. 409-414. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-32/