Volume 65, Number 2, January 2004
|Page(s)||151 - 157|
|Published online||01 January 2004|
Leadership statistics in random structures
Theoretical Division and Center for Nonlinear Studies Los Alamos National Laboratory - Los Alamos, NM, 87545 USA
2 Center for Polymer Studies and Department of Physics Boston University - Boston, MA, 02215 USA
Accepted: 18 November 2003
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.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75.Hc – Networks and genealogical trees
© EDP Sciences, 2004
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