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. 
@article{DM_2022_34_2_a9,
     author = {E. V. Khvorostyanskaya},
     title = {Limit theorems for the maximal tree size of a {Galton\,--\,Watson} forest in the critical case},
     journal = {Diskretnaya Matematika},
     pages = {120--136},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_2_a9/}
}
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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/