Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

Hassan Chhaiba (1) , Nizar Demni (2) , Zouhair Mouayn (3)

1 Ibntofail University, Morocco
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Faculte des sciences et techniques Beni Mellal

To each hyperbolic Landau level of the Poincar\'e disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its 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 determine the L\'evy-Kintchine decomposition 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-L\'evy measure, we introduce a new infinitely-divisible distribution for which we derive the characteristic function.

Mots clés: hyperbolic Landau levels; Lévy-Kintchine representation; generalized binomial distributions; quasi-infinitely-divisible distributions; quasi-Lévy measures

Domaines: Probabilités [math.PR]

Hassan Chhaiba, Nizar Demni, Zouhair Mouayn. Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels. Journal of Mathematical Physics, 2016, 57 (7), ⟨10.1063/1.4958724⟩. ⟨hal-01278768⟩