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Leadership Statistics in Random Structures

E. Ben-Naim·P. L. Krapivsky
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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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E. Ben-Naim, P. L. Krapivsky. 2003-07-30. Leadership Statistics in Random Structures. https://doi.org/10.1209/epl%2Fi2003-10081-7

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