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.

Locations

• EPL (Europhysics Letters) - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View