Leadership statistics in random structures
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.
- Publication:
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EPL (Europhysics Letters)
- Pub Date:
- January 2004
- DOI:
- 10.1209/epl/i2003-10081-7
- arXiv:
- arXiv:cond-mat/0307744
- Bibcode:
- 2004EL.....65..151B
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 5 pages, 3 figures