Ulysse Marquis — University of Trento - FBK #
Statistical physics of city growth #
Cities keep growing and host more than half of the global population. Despite their importance, there are no robust empirical laws describing city spatial dynamics. In [1], employing recent remote sensing data, we studied the growth of 19 cities over 30 years using population as control variable. When focusing on the largest component, we find that variations of population and built area are essentially proportional. However, when looking in a given direction, there are strong deviations to the square-root law expected in the isotropic case. By employing the framework of surface growth, we reveal that cities interface follow are anomalously intrinsically rough. Their local roughness is characterized by a scaling exponent equal to about 0.54. Other exponents are widely spread. We also observed seemingly universal, stretched-exponential fluctuations. These observations raise many physical questions; we discuss some of them concerning surface growth through strongly polydisperse deposition in [2]; a recent modified Eden based model reproducing the empirically observed results was proposed in [3]. [1] Marquis, U., Artime, O., Gallotti, R., & Barthelemy, M. (2025). Universal Roughness and the Dynamics of Urban Expansion. Phys. Rev. Lett., 135(18), 187403. [2] Marquis, U., Gallotti, R., & Barthelemy, M. (2026). Beyond dynamic scaling: rare events break universality. https://arxiv.org/abs/2604.01820 [3] Hendrick, M., Trique, M., & Manoli, G. (2026). Disorder Crossover in Urban-Front Growth. https://arxiv.org/abs/2604.21437