2018/07/18 by Stefano Gualandi, Giuseppe Toscani · 20 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Complex Network Analysis Techniques #Demography #Diffusion #Econometrics #Economic geography #Economics #Emigration #Kinetic energy #Law #Log-normal distribution #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Pareto distribution #Pareto principle #Physics #Population #Population size #Power law #Sociology #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #Urban agglomeration #Variable (mathematics) #Zipf's law #msc:35Q91 #msc:82B40 #msc:91D10 #msc:97MXX #nlin.AO #physics.soc-ph
paper · pdf · doi:10.1016/j.physa.2019.04.260
published in Physica A Statistical Mechanics and its Applications 524, 221-234 (Elsevier BV)
arxiv created 2018/07/18 · openalex publication_date 2019/04/26 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration. In most cases, the Boltzmann-type kinetic description allows to obtain, within an asymptotic procedure, a Fokker--Planck equation with variable coefficients of diffusion and drift, which describes the evolution in time of some probability density of the city size. It is shown that, in dependence of the microscopic rules of migration, the equilibrium density can follow both a power law for large values of the size variable, which contains as particular case a Zipf's law behavior, and a lognormal law for middle and low values of the size variable. In particular, connections between the value of Pareto index of the power law at equilibrium and the disposal of the population to emigration are outlined. The theoretical findings are tested with recent data of the populations of Italy and Switzerland.