Open AccessExtreme fluctuations in noisy task-completion landscapes on scale-free networks
Author(s) -
Hasan Güçlü,
G. Korniss,
Zoltán Toroczkai
Publication year - 2007
Publication title -
chaos an interdisciplinary journal of nonlinear science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.971
H-Index - 113
eISSN - 1089-7682
pISSN - 1054-1500
DOI - 10.1063/1.2735446
Subject(s) - gumbel distribution , computer science , limit (mathematics) , scale (ratio) , task (project management) , extreme value theory , synchronization (alternating current) , statistical physics , scaling , queueing theory , scale free network , linear scale , complex network , topology (electrical circuits) , theoretical computer science , mathematics , statistics , physics , mathematical analysis , computer network , geometry , geodesy , quantum mechanics , combinatorics , world wide web , geography , management , economics
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
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