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On random mappings with a single attracting centre

Published online by Cambridge University Press:  14 July 2016

Ljuben R. Mutafchiev
Ljuben R. Mutafchiev*
Affiliation:
Institute of Mathematics, Sofia
*
∗Postal address: Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, 1090 Sofia, Bulgaria.
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Abstract

We consider the random vector T = (T(0), ···, T(n)) with independent identically distributed coordinates such that Pr{T(i) = j} = Pj, j = 0, 1, ···, n, Σ . A realization of T can be viewed as a random graph GT with vertices {0, ···, n} and arcs {(0, T(0)), ···, (n, T(n))}. For each T we partition the vertex-set of GT into three disjoint groups and study the joint probability distribution of their cardinalities. Assuming that we observe the asymptotics of this distribution, as n → ∞, for all possible values of P0. It turns out that in some cases these cardinalities are asymptotically independent and identically distributed.

Keywords

RANDOM GRAPHSLIMITING DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 258 - 264
Copyright
Copyright © Applied Probability Trust 1987 

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