Universality class of urban expansion

Establish whether the large-scale statistical behavior of urban perimeter growth and interface roughening belongs to any established universality class of surface growth (such as Edwards–Wilkinson, Kardar–Parisi–Zhang, or Mullins–Herring), or instead defines a new universality class specific to urban expansion dynamics.

Background

The review connects urban sprawl to interface growth in statistical physics, highlighting measured roughness exponents, anomalous scaling, and coalescence mechanisms that resemble known growth processes. Despite these parallels, empirical exponents do not match canonical thermal or quenched classes cleanly, and cities display strong anisotropy and heterogeneous growth modes (local accretion versus coalescence).

Given these findings, the authors point to the need for a more definitive classification of urban expansion within the framework of universality classes. Doing so would clarify whether urban growth is governed by the same invariant mechanisms as classical surface growth models or whether it necessitates a distinct universality class, thereby informing both theory and empirical analysis.