Abstract:
Galton–Watson trees formed by a critical branching process are considered. The distribution of the number of immediate descendants of the particles in the process has infinite variance. The limit distribution of the number of vertices in the lower layers of a tree is found as the number of vertices approaches infinity.
Keywords:Galton–Watson tree, critical branching process, tree layer,
limit distribution.
This work was supported
by the Federal Budget Fund for the fulfillment
of the State Assignment of the KarSC Russian Academy of Sciences
(Institute of Applied Mathematical
Research of the KarSC Russian Academy of Sciences).
Citation:
Yu. L. Pavlov, “On the limit distribution of the number of vertices in the levels of a Galton–Watson tree”, Mat. Zametki, 116:3 (2024), 430–437; Math. Notes, 116:3 (2024), 514–520
\Bibitem{Pav24}
\by Yu.~L.~Pavlov
\paper On the limit distribution of the number of vertices in the levels of a~Galton--Watson tree
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 3
\pages 430--437
\mathnet{http://mi.mathnet.ru/mzm14254}
\crossref{https://doi.org/10.4213/mzm14254}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 3
\pages 514--520
\crossref{https://doi.org/10.1134/S0001434624090104}
Citation in format AMSBIB
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