Power-law size distribution of supercritical random trees
Paolo De Los Rios
Abstract
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.
Create a lesson
Related papers
Robust Golden Ratio universality as a consequence of a circulant symmetry
Luka Paljk, Johannes Schmidt, Vladislav Popkov
Replica Transition at Measurement-Altered Ising Criticality
Kabir Khanna, Sara Murciano, Romain Vasseur
Scalene Yang-Baxter triples realize all nearest-neighbour Hamiltonians with global additive symmetries
Pramod Padmanabhan, Somnath Maity, Akash Sinha et al.
Graph-theoretic framework for semi-Markov networks: transient and stationary occupation probabilities, hitting times and weak ergodicity breaking
Julian Voits
Spectral optimization of spherical lattices and applications to classical and quantum interacting spin systems
Jonas Völler, Grigorios Makris, Fabian Hassler et al.
Entropic-ordered superfluid
Isabella Zane, Andrew Lucas