Cities as evolutionary systems in random media

The purpose of the paper is to discuss some potential applications of random media theory to urban modelling, with the emphasis on the intermittency phenomenon. The moment test of intermittency is explained using the model of continuous-time branching random walk on the integer lattice Z^d with random branching rates. Statistical moments of the population density are studied using a Cauchy problem for the Anderson operator with random potential. The Feynman–Kac representation of the solution is discussed, and Lyapunov exponents responsible for the super-exponential growth of the moments are evaluated. The higher-order Lyapunov exponents are also obtained. The results suggest that the higher-order intermittency is reduced, in a sense, to that of the mean population density.