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We study the statistics and scaling of extreme fluctuations in noisytask-completion landscapes, such as those emerging in synchronizeddistributed-computing networks, or generic causally-constrained queuingnetworks, with scale-free topology. In these networks the average size of thefluctuations becomes finite (synchronized state) and the extreme fluctuationstypically diverge only logarithmically in the large system-size limit ensuringsynchronization in a practical sense. Provided that local fluctuations in thenetwork are short-tailed, the statistics of the extremes are governed by theGumbel distribution. We present large-scale simulation results using the exactalgorithmic rules, supported by mean-field arguments based on a coarse-graineddescription.Comment: 16 pages, 6 figures, revte

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