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Leadership statistics in random structures

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2004 EDP Sciences
, , Citation E. Ben-Naim and P. L. Krapivsky 2004 EPL 65 151 DOI 10.1209/epl/i2003-10081-7

0295-5075/65/2/151

Abstract

The largest component ("the leader") in evolving random structures often exhibits universal statistical properties. This phenomenon is demonstrated analytically for two ubiquitous structures: random trees and random graphs. In both cases, lead changes are rare as the average number of lead changes increases quadratically with logarithm of the system size. As a function of time, the number of lead changes is self-similar. Additionally, the probability that no lead change ever occurs decays exponentially with the average number of lead changes.

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10.1209/epl/i2003-10081-7