## Abstract

To each hyperbolic Landau level of the Poincaré disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we derive a Lévy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-Lévy measure, we introduce a new infinitely divisible distribution for which we derive the characteristic function. Published by AIP Publishing.

Original language | English (US) |
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Article number | 0721031 |

Journal | Journal of Mathematical Physics |

Volume | 57 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2016 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics