Geodesic
A remark on Galton--Watson forests
Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 47-59

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We demonstrate that the limit theorems on basic characteristics of the Galton–Watson random forests established earlier hold true provided that there exists the second moment of the distribution of offspring of a single particle of the critical branching process that generates the forest. 
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     author = {N. I. Kazimirov and Yu. L. Pavlov},
     title = {A remark on {Galton--Watson} forests},
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     year = {2000},
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N. I. Kazimirov; Yu. L. Pavlov. A remark on Galton--Watson forests. Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 47-59. http://geodesic.mathdoc.fr/item/DM_2000_12_1_a3/