Extreme fluctuations in noisy task-completion landscapes on scale-free networks

Details Extreme fluctuations in noisy task-completion landscapes on scale-free networks Extreme fluctuations in noisy task-completion landscapes on scale-free networks

2007-01-13

arxiv.org/abs/cond-mat/0701301v1

Chaos 17, 026104 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, 6 figures, revtex

Scientific paper

10.1063/1.2735446

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.

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