Amazing collaboration with brilliant co-authors Benjamin F. Maier (also the artist behind the figure below) & @sunelehmann.com

Looking forward to your thoughts, and let me know if you’d like to collaborate on follow-up work on mobility and the pair distribution function!

Mobility within a city is governed by one power law (which tells us that distance matters less), while another, steeper power law describes moves between cities, reflecting the stronger deterrent of greater distances.

When considering mobility centered around a single city — rather than mobility of an entire country — a more nuanced picture emerges. Instead of a simple global power law, we observed a universal piecewise behavior.

Finally, we link these findings to the well-studied gravity model by extending it to a continuous setting that does not rely on arbitrary administrative units. However, the story does not end here.

The fractal shape of cities explains the meso-scale of the pairwise distance distribution; and at the large scale, we show that city positions are indistinguishable from uniformly random.

Using the pair distribution function, we treat addresses as particles and develop a statistical physics of locations, from the micro-scale of buildings to the macro-scale of cities. By modeling buildings as an ideal gas in a potential, we reproduce local urban densities.

By using a simple tool from physics—the pair distribution function—we separate the influence of geography (coastlines, rivers, road networks) from people’s mobility choices. Once you factor out the map, the remaining behaviour follows a striking, universal power law across five orders of magnitude.