Leadership Statistics in Random Structures
arXiv:cond-mat/0307744 · doi:10.1209/epl/i2003-10081-7
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.
5 pages, 3 figures
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