Renormalization group evaluation of exponents in family name distributions

TL;DR

This paper uses renormalization group methods to analyze how family name distributions follow power laws, linking the exponent to population growth and name creation rates.

Contribution

It introduces a novel approach by representing the Galton-Watson process in Hilbert space and applying renormalization group techniques to explain the origin of power law exponents.

Findings

Power law distribution of family names explained by the model

Exponent related to population growth and name production rates

Method provides a theoretical basis for observed name frequency patterns

Abstract

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 space, and its time evolution may be analyzed by renormalization group techniques, thus explaining the origin of the power law and establishing the connection between its exponent and the ratio between the population growth and the name production rates.