Limit distributions of many-particle spectra and $q$-deformed Gaussian variables

Tom 73 / 2006

Piotr Śniady Banach Center Publications 73 (2006), 409-414 MSC: 81V35, 81V70, 15A52. DOI: 10.4064/bc73-0-32

Streszczenie

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 ${k}/{\sqrt{n}}$. 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 \cite{W1,W2}, Mon and French \cite{MF}.

Autorzy

  • Piotr ŚniadyInstitute of Mathematics
    University of Wroc/law
    Pl. Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail

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