Growth over time-correlated disorder: a spectral approach to Mean-field

Abstract

We generalize a model of growth over a disordered environment, to a large class of Itō processes. In particular, we study how the microscopic properties of the noise influence the macroscopic growth rate. The present model can account for growth processes in large dimensions, and provides a bed to understand better the trade-off between exploration and exploitation. An additional mapping to the Schrördinger equation readily provides a set of disorders for which this model can be solved exactly. This mean-field approach exhibits interesting features, such as a freezing transition and an optimal point of growth, that can be studied in details, and gives yet another explanation for the occurrence of the $\text{Zipf law}$ in complex, well-connected systems.

10 pages + Appendix

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Cited by in corpus (1)

• The balance of growth and risk in population dynamics