naa a22 4500 510812163 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060175 doi (NATIONALLICENCE)springer-10.1134/S0081543813060175 Limit distributions of the number of loops in a random configuration graph [Elektronische Daten] [Yu. Pavlov, M. Stepanov] We consider a random graph constructed by the configuration model with the degrees of vertices distributed identically and independently according to the law P(ξ≥k), k = 1, 2, ..., with τ ∈ (1, 2). Connections between vertices are then equiprobably formed in compliance with their degrees. This model admits multiple edges and loops. We study the number of loops of a vertex with given degree d and its limiting behavior for different values of d as the number N of vertices grows. Depending on d = d(N), four different limit distributions appear: Poisson distribution, normal distribution, convolution of normal and stable distributions, and stable distribution. We also find the asymptotics of the mean number of loops in the graph. Pleiades Publishing, Ltd., 2013 Pavlov Yu Institute of Applied Mathematical Research, Karelian Research Centre of the Russian Academy of Sciences, Pushkinskaya ul. 11, 185910, Petrozavodsk, Russia aut Stepanov M. Department of Mathematics, Åbo Akademi University, Fänriksgatan 3, ASA B, 3:e vån, 20500, Åbo, Finland aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 202-219 0081-5438 282:1<202 2013 282 11501 https://doi.org/10.1134/S0081543813060175 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060175 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pavlov Yu Institute of Applied Mathematical Research, Karelian Research Centre of the Russian Academy of Sciences, Pushkinskaya ul. 11, 185910, Petrozavodsk, Russia aut NATIONALLICENCE 700 1- Stepanov M. Department of Mathematics, Åbo Akademi University, Fänriksgatan 3, ASA B, 3:e vån, 20500, Åbo, Finland aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 202-219 0081-5438 282:1<202 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer