Analysis of generalized Poisson distributions associated with higher Landau levels

作者：Demni Nizar^*; Mouayn Zouhair^*

来源：Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2015, 18(4): 1550028.

DOI：10.1142/S0219025715500289

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

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 F-2(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 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.

• 出版日期2015-12