Abstract:
We prove two theorems which give conditions for absence of a giant component
in the generalised allocation scheme and present a series of examples. This research was supported by the Russian Foundation for Basic Research,
grant 00–01–00233.
Received: 17.01.2002
Bibliographic databases:
UDC:519.2
Language: Russian
Citation:
N. I. Kazimirov, “On some conditions for the absence of a giant component in a generalized allocation scheme”, Diskr. Mat., 14:2 (2002), 107–118; Discrete Math. Appl., 12:3 (2002), 291–302
\Bibitem{Kaz02}
\by N.~I.~Kazimirov
\paper On some conditions for the absence of a giant component in a generalized allocation scheme
\jour Diskr. Mat.
\yr 2002
\vol 14
\issue 2
\pages 107--118
\mathnet{http://mi.mathnet.ru/dm245}
\crossref{https://doi.org/10.4213/dm245}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1937012}
\zmath{https://zbmath.org/?q=an:1046.60018}
\transl
\jour Discrete Math. Appl.
\yr 2002
\vol 12
\issue 3
\pages 291--302
Linking options:
https://www.mathnet.ru/eng/dm245
https://doi.org/10.4213/dm245
https://www.mathnet.ru/eng/dm/v14/i2/p107
This publication is cited in the following 7 articles:
Svante Janson, “Simply generated trees, conditioned Galton–Watson trees, random allocations and condensation”, Probab. Surveys, 9:none (2012)
E. S. Bernikovich, Yu. L. Pavlov, “On the maximum size of a tree in a random unlabelled unrooted forest”, Discrete Math. Appl., 21:1 (2011), 1–21
Erlihson M.M., Granovsky B.L., “Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case”, Annales de l Institut Henri Poincare-Probabilites et Statistiques, 44:5 (2008), 915–945
A. V. Kolchin, V. F. Kolchin, “On transition of distributions of sums of independent identically distributed random variables from one lattice to another in the generalised allocation scheme”, Discrete Math. Appl., 16:6 (2006), 527–540
Yu. L. Pavlov, “Limit theorems on sizes of trees in a random unlabelled forest”, Discrete Math. Appl., 15:2 (2005), 153–170
N. I. Kazimirov, “The occurrence of a gigantic component in a random permutation with a known number of cycles”, Discrete Math. Appl., 13:5 (2003), 523–535
A. V. Kolchin, “On limit theorems for the generalised allocation scheme”, Discrete Math. Appl., 13:6 (2003), 627–636
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