Conceptual proofs of L log L criteria for mean behavior of branching processes

@article{Lyons1995ConceptualPO,
  title={Conceptual proofs of L log L criteria for mean behavior of branching processes},
  author={Russell Lyons and Robin Pemantle and Yuval Peres},
  journal={Annals of Probability},
  year={1995},
  volume={23},
  pages={1125-1138}
}
The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least n generations. We give conceptual proofs of these theorems based on comparisons of Galton-Watson measure to another measure on the space of trees. This approach also explains Yaglom's… 

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