title: Scale-free behavior and universality in random fragmentation and aggregation.
abstract: Two distinct mechanisms underlying the existence of power-law distributions are presented: the distribution is stationary under the process of merging and splitting of classes and the distribution of the entities under study is invariant under changes of the classification scheme. We provide an explanation for the ubiquitous inverse n relationship in the species abundance relationship in ecology and the 1/n(2) distribution of company sizes based on the minimum impact principle.
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Jayanth R
authors.initials: JR
authors.lastname: Banavar
authors.forename: Paolo
authors.initials: P
authors.lastname: De los Rios
authors.forename: Alessandro
authors.initials: A
authors.lastname: Flammini
authors.forename: Neal S
authors.initials: NS
authors.lastname: Holter
authors.forename: Amos
authors.initials: A
authors.lastname: Maritan