Leadership Statistics in Random Structures

Details Leadership Statistics in Random Structures Leadership Statistics in Random Structures

2003-07-30

arxiv.org/abs/cond-mat/0307744v1

Europhys. Lett. 65, 151 (2004)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1209/epl/i2003-10081-7

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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