The City as a Complex System. Statistical Physics and Agent-Based Simulations on Urban Models

Overview & Synopsis

Social and natural sciences share an interest for collective phenomena, which constitute an important part of the domain of complex systems. This thesis focuses on the study of urban systems, using analytical tools inspired by statistical physics, and also simulations, in particular agent-based models. A first analytical resolution of a Schelling spatial segregation model is presented, using a statistical physics framework linking individual and collective dynamics. This framework shows that utility or welfare in socio-economic models corresponds to a chemical potential in physics, a correspondence which is applied to a urban housing model. The housing market is further studied with a parsimonious price formation model. The implementation of an agent-based model, which reproduces the results of the standard urban economics (AMM) model, provides a second point of view on urban systems and the interaction between transport and land use. The simulations give results also when analytical resolution is lacking. The model is used to study the economic, environmental and social outcomes of having an amenity in the urban area and of polycentric cities. With two income groups, this work provides insights on the different urban social structures in North American and European cities for instance.