Space-time correlations in urban population flows

TL;DR

This paper uncovers regular patterns in urban population flows, showing distance and time correlations that follow specific laws, and introduces a dynamical model that explains these phenomena and identifies collective growth modes.

Contribution

It presents a novel dynamical model for city population growth that explains observed space-time correlations and identifies collective growth modes.

Findings

Distance correlations follow an inverse square law with a 74 km scale.

Time correlations decay exponentially with a 17.2-year characteristic time.

Numerical simulations confirm the model's applicability and reveal collective growth modes.

Abstract

Evidences are presented concerning tantalizing regularities in cities' population-flows in what regards to space and time correlations. The former exhibit a distance-behavior (for large distances) compatible with the inverse square law, following an overall Lorentzian dependence with an scale-parameter of $74\pm6$ km. The later decay exponentially with a characteristic time of $17.2\pm1.3$ years. These features can be explained by a dynamical model for cities' population-growth of a Lagevinian nature. Numerical simulations based on the model confirm its applicability. The model also allows for the identification of collective normal modes of city-growth dynamics that can be empirically identified.