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Analysis of generalized Poisson distributions associated with higher Landau levels

IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France

E-mail Address: nizar.demni@univ-rennes1.fr

and

Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane, P. O. Box 523, Béni Mellal, Morocco

E-mail Address: mouayn@fstbm.ac.ma

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https://doi.org/10.1142/S0219025715500289Cited by:13 (Source: Crossref)

Abstract

To a higher Landau level corresponds a generalized Poisson distribution arising from generalized coherent states. In this paper, we write down the atomic decomposition of this probability distribution and express its probability mass function as a $_{2} F_{2}$ $_{2} F_{2}$ -hypergeometric polynomial. Then, we prove that it is not infinitely divisible in contrast with the Poisson distribution corresponding to the lowest Landau level. We also derive a Lévy–Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that the representative measure is a quasi-Lévy measure. By considering the total variation of this last measure, we obtain the characteristic function of a new infinitely divisible discrete probability distribution for which we also compute the probability mass function.

Communicated by F. Fagnola

Keywords:

AMSC: 81V80, 60E99

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