Disorder Crossover in Urban-Front Growth
Abstract
Urban expansion fronts display a robust local roughness exponent together with strongly dispersed growth and nonuniversal dynamic exponents. We show that this coexistence can arise from a disorder-controlled crossover in projected-front growth. Introducing a minimal Eden model, in which geographic constraints act as quenched dilution and coalescence as quenched local acceleration, we demonstrate that the resulting front enters a long disorder-dominated preasymptotic regime, whose scaling near threshold is set by ordinary two-dimensional percolation. In this regime, the local roughness remains close to , while the large-scale exponents vary broadly with disorder and acceleration. These results provide a minimal explanation of urban-front roughening and suggest a more general mechanism for stochastic growth in heterogeneous media.
Cite
@article{arxiv.2604.21437,
title = {Disorder Crossover in Urban-Front Growth},
author = {Martin Hendrick and Maximilian Trique and Gabriele Manoli},
journal= {arXiv preprint arXiv:2604.21437},
year = {2026}
}