Geodesic
Limit theorems for the maximal tree size of a Galton\,--\,Watson forest in the critical case
Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 120-136.

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We consider a critical Galton – Watson branching process starting with $N$ particles; the number of offsprings is supposed to have the distribution $p_k=(k+1)^{-\tau}-(k+2)^{-\tau}$, $k=0,1,2,\ldots$ Limit distributions of the maximal tree size are obtained for the corresponding Galton – Watson forest with $N$ trees and $n$ non-root vertices as $N,n\to\infty$, $n/N^{\tau}\geq C> 0$.
Keywords: Galton – Watson forest, maximal tree size, limit distribution. 
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E. V. Khvorostyanskaya. Limit theorems for the maximal tree size of a Galton\,--\,Watson forest in the critical case. Diskretnaya Matematika, Tome 34 (2022) no. 2, pp. 120-136. http://geodesic.mathdoc.fr/item/DM_2022_34_2_a9/

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