According to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law. We show that the Galton–Watson process corresponding to the dynamics of a growing population can be represented in Hilbert...

The purpose of this paper is the application of a usual method of statistical mechanics—the renormalization based on Wilson's recursive relations—in order to study the critical behavior of a social index, namely the live births per 1000 population. The drastic decreases of this index on...