Cities as Evolutionary Systems in Random Media

  • Leonid Bogachev


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 ℤd 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.


Random Walk Lyapunov Exponent Random Medium Moment Lyapunov Exponent Punov Exponent 


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© Physica-Verlag Heidelberg and Accademia di Architettura, Mendrisio, Switzerland 2008

Authors and Affiliations

  • Leonid Bogachev
    • 1
  1. 1.Department of StatisticsUniversity of LeedsUK

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