A Spatially Extended Model for Residential Segregation

In this paper we analyze urban spatial segregation phenomenon in terms of the income distribution over a population, and inflationary parameter weighting the evolution of housing prices. For this, we develop a discrete, spatially extended model based in a multi--agent approach. In our model, the mobility of socioeconomic agents is driven only by the housing prices. Agents exchange location in order to fit their status to the cost of their housing. On the other hand, the price of a particular house changes depends on the status of its tenant, and on the neighborhood mean lodging cost, weighted by a control parameter. The agent's dynamics converges to a spatially organized configuration, whose regularity we measured by using an entropy--like indicator. With this simple model we found a nontrivial dependence of segregation on both, the initial inequality of the socioeconomic agents and the inflationary parameter. In this way we supply an explanatory model for the segregation--inequality thesis putted forward by Douglas Massey.Comment: 17 pages, 11 figures. email: [email protected], [email protected]

Projection of Markov measures may be Gibbsian

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Holder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.Comment: 4 latex figure