Power law size distribution of supercritical random trees
Institut de Physique Théorique,
Université de Lausanne CH-1015 Dorigny-Lausanne, Switzerland
Accepted: 1 October 2001
The probability distribution P(k) of the sizes k of critical trees (branching ratio m=1) is well known to show a power law behavior . Such behavior corresponds to the mean-field approximation for many critical and self-organized critical phenomena. Here we show numerically and analytically that also supercritical trees (branching ration m> 1) are "critical" in that their size distribution obeys a power law k-2. We mention some possible applications of these results.
PACS: 89.75.Da – Systems obeying scaling laws / 89.75.-k – Complex systems / 89.90.+n – Other topics in areas of applied and interdisciplinary physics
© EDP Sciences, 2001