Urban growth and the emergent statistics of cities

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Science Advances  19 Aug 2020:
Vol. 6, no. 34, eaat8812
DOI: 10.1126/sciadv.aat8812


Urban theory models cities as spatial equilibria to derive their aggregate properties as functions of extensive variables, such as population size. However, this assumption seems at odds with cities’ most interesting properties as engines of fast and variable processes of growth and change. Here, we build a general statistical dynamics of cities across scales, from single agents to entire urban systems. We include agents’ strategic behavior to produce predictable growth rates, which requires balancing relative incomes and costs over time. We implement these dynamics using stochastic differential equations and control theory to demonstrate a number of general emergent properties of cities deriving from limit theorems applied to growth rates. This framework establishes necessary conditions for scaling to be conserved by urban dynamics and shows how exponent corrections can be calculated. These ideas are tested using stochastic simulations and a long timeseries for 382 US Metropolitan Areas over nearly five decades.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

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