Power law size distribution of supercritical random trees
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 k(-3/2). 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.
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De Los Rios, P. (2001). Power law size distribution of supercritical random trees. Europhysics Letters - European Physical Society Letters (EPL), 56, 898–903. https://doi.org/10.1209/epl/i2001-00604-2
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2001
56
898
903
REVIEWED
EPFL