2012/09/23 by David Aldous, Aldous, David, Bowen Huang +1
Economics, Econometrics and Finance · Physics and Astronomy · #60D05 #91B72 #Data Analysis #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Regional Economics and Spatial Analysis #Statistics and Probability (physics.data-an) #msc:60D05 #msc:91B72 #physics.data-an #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.1209.5120
arxiv created 2012/09/23 · openalex publication_date 2012/09/23 · arxiv updated 2012/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a model in which city populations grow at rates proportional to the area of their "sphere of influence", where the influence of a city depends on its population (to power α) and distance from city (to power -β) and where new cities arise according to a certain random rule. A simple non-rigorous analysis of asymptotics indicates that for β> 2α the system exhibits "balanced growth" in which there are an increasing number of large cities, whose populations have the same order of magnitude, whereas for β< 2α the system exhibits "unbalanced growth" in which a few cities capture most of the total population. Conceptually the model is best regarded as a spatial analog of the combinatorial "Chinese restaurant process".