## 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 2F2-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 Levy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that the representative measure is a quasi-Levy 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.

Original language | English (US) |
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Article number | 1550028 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2015 |

## Keywords

- Generalized Poisson distributions
- higher Landau levels
- Laguerre polynomials
- quasi-infinitely divisible

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics