Geodesic
Sizes of Trees in a Random Forest and Configuration Graphs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 298-315

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We consider Galton–Watson random forests with $N$ rooted trees and $n$ nonroot vertices. The distribution of the number of offspring of the critical homogeneous branching process generating a forest has infinite variance. Such branching processes are used in the study of the structure of random configuration graphs designed for simulating complex communication networks. We prove theorems on the limit distributions of the number of trees of a given size for various relations between $N$ and $n$ as they tend to infinity. 
@article{TM_2022_316_a19,
     author = {Yu. L. Pavlov and I. A. Cheplyukova},
     title = {Sizes of {Trees} in a {Random} {Forest} and {Configuration} {Graphs}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {298--315},
     publisher = {mathdoc},
     volume = {316},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_316_a19/}
}
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Yu. L. Pavlov; I. A. Cheplyukova. Sizes of Trees in a Random Forest and Configuration Graphs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 298-315. http://geodesic.mathdoc.fr/item/TM_2022_316_a19/