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Invariance and attraction properties of Galton-Watson trees
[article]
2020
arXiv
pre-print
We give a description of invariants and attractors of the critical and subcritical Galton-Watson tree measures under the operation of Horton pruning (cutting tree leaves with subsequent series reduction). Under a regularity condition, the class of invariant measures consists of the critical binary Galton-Watson tree and a one-parameter family of critical Galton-Watson trees with offspring distribution {q_k} that has a power tail q_k∼ Ck^-(1+1/q_0), where q_0∈(1/2,1). Each invariant measure has
arXiv:1911.08095v3
fatcat:yaqersagxbcfdinr65ewwrfzfi