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

Thomas Gueudré

doi:10.1103/physreve.95.042134

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arXiv · 1612.05463

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

Thomas Gueudré

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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 $\textit{Zipf law}$ in complex, well-connected systems.

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Thomas Gueudré. 2016-12-16. Growth over time-correlated disorder: a spectral approach to Mean-field. https://doi.org/10.1103/physreve.95.042134

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