Modeling Local Social Migrations: A Cellular Automata Approach

Abstract

In local social migrations, agents move from their initial location looking for a better local social environment. Social migrations processes do not change the number of social agents of a given type (i.e., the empirical distribution of the population) but their spatial location. Although cellular automata seems to appear as a natural approach to model of social migrations, the evolution of the configuration through a cellular automata might induce a new configuration wherein the number of agents of each type might be actually modified. This article provides a characterization of these cellular automata rules such that for any initial empirical distribution, the evolution of the configuration through a cellular automata of such class induces a new configuration with the same empirical distribution as the initial one, as required to model local social migrations. A class of sequences is defined in order to establish a sufficient condition to maintain this invariance property.