Generalized Poisson ensemble

Abstract

A generalized Poisson ensemble is constructed using the maximum entropy principle based on the non-extensive entropy. It is found that the correlations which are introduced among the eigenvalues lead to statistical distributions with heavy tails. As a consequence, long-range statistics, measured by the number variance, show super-Poissonian behavior and the short-range ones, measured by the nearest-neighbor-distribution show, with respect to Poisson, enhancement at small and large separations. Potential applications were found for the sequence data of protein and DNA, which display good agreement with the model. In particular, the ensuing parameter λ of the generalized Poisson ensemble can be utilized to facilitate protein classification.