2003/07/30 by E. Ben-Naim, E Ben-Naim, P. L. Krapivsky +1 · 1 citation
Physics and Astronomy · #Complex Network Analysis Techniques #Origins and Evolution of Life #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1209/epl/i2003-10081-7
published as Europhys. Lett. 65, 151 (2004) · 5 pages, 3 figures
arxiv created 2003/07/30 · openalex publication_date 2004/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.