Geodesic
Limit distributions of the number of vertices of a~given degree in a~configuration graph with bounded number of edges
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 468-486

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We consider the model of an $N$-vertex configuration graph where the number of edges is at most $n$ and the degrees of vertices are independent and identically distributed (i.i.d.) random variables (r.v.'s). The distribution of the r.v. $\xi$, which is defined as the degree of any given vertex, is assumed to satisfy the condition $p_k=\mathbf{P}\{\xi=k\}\sim\frac{L}{k^g\ln^h k}$ as $k\to\infty$, where $L>0$, $g>1$, $h\ge0$. Limit theorems for the number of vertices of a given degree as $N, n\to\infty$ are proved.
Mots-clés : configuration graph, limit distribution.
Keywords: degree of a vertex 
@article{TVP_2021_66_3_a3,
     author = {Yu. L. Pavlov and I. A. Cheplyukova},
     title = {Limit distributions of the number of vertices of a~given degree in a~configuration graph with bounded number of edges},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {468--486},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a3/}
}
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Yu. L. Pavlov; I. A. Cheplyukova. Limit distributions of the number of vertices of a~given degree in a~configuration graph with bounded number of edges. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 468-486. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a3/