Download Power-law performance ranking relationship in exponentially

NSPCS2014
Power-law performance ranking relationship in exponentially growing
populations
Lei-Han Tang, Hong Kong Baptist University
The Zipf’s law describing fat tails in size distributions is ubiquitous among diverse economic
and social datasets[1]. Despite the surge of theoretical activities in the past decade, few have
examined the phenomena from the viewpoint of growth with size-independent updating rules
that lead to scale-free behavior. Through a detailed analysis of the entry and exit patterns of
computers on the TOP500 lists over the last 21 years, we propose a dynamical model for the
population in which performances of existing computers are copied, improved or retired
following a probabilistic rule[2]. We show that the model can be mapped exactly to the
randomly branching tree problem in statistical physics. This mapping leads to a population
dynamics equation, which affords a traveling front solution in performance space. The velocity
and the exponential shape of the traveling front can be used directly to determine the
performance growth rate and the performance-rank power law exponent respectively. The treelike evolution dynamics also implies that the performance fluctuation decays with rank as a
power-law. Our study offers a quantitative framework to relate the (stochastic) individual-level
performance shift to the population-level rank distribution which could be of interest in a broad
range of ecological, social and economic contexts.
*Work supported in part by the RGC/NSFC under grant N-HKBU 213/10.
[1] M. E. J. Newman, Contemporary Phys. 46:323-351 (2005).
[2] C. Cai, D.-L. Li, Q. Ouyang, L.-H. Tang and Y. Tu, to be published.
Korea Institute for Advanced Study
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