Hierarchical noise in large systems of independent agents

Abstract

A generalization of the coherent-noise models [M. E. J. Newman and K. Sneppen, Phys. Rev. E{\bf54}, 6226 (1996)] is presented where the agents in the model are subjected to a multitude of stresses, generated in a hierarchy of different contexts. The hierarchy is realized as a Cayley-tree. Two different ways of stress propagation in the tree are considered. In both cases, coherence arises in large subsystems of the tree. Clear similarities between the behavior of the tree model and of the coherent-noise model can be observed. For one of the two methods of stress propagation, the behavior of the tree model can be approximated very well by an ensemble of coherent-noise models, where the sizes $k$ of the systems in the ensemble scale as $k^{-2}$. The results are found to be independent of the tree's structure for a large class of reasonable choices. Additionally, it is found that power-law distributed lifetimes of agents arise even under the complete absence of correlations between the stresses the agents feel.