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Random mappings with an attracting center: Lagrangian distributions and a regression function

Published online by Cambridge University Press:  14 July 2016

Sven Berg  and
Ljuben Mutafchiev
Sven Berg*
Affiliation:
Lund University
Ljuben Mutafchiev*
Affiliation:
Bulgarian Academy of Sciences
*
∗Postal address: Department of Statistics, University of Lund, Box 7008, S-220 07 Lund, Sweden.
∗∗Postal address: Bulgarian Academy of Sciences, Institute of Mathematics, 1090 Sofia P.O. Box 373, Bulgaria.
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Abstract

For a random mapping model with a single attracting center (Stepanov (1971)) we study the relationship between the sizes of the central tree, the adjacent points, and the free points. Joint, marginal and conditional distributions are shown to be of well-known Lagrangian type. Exact and asymptotic moment properties are investigated with the aid of Riordan's (1968) Abel identities. In particular, the relationship between the size of the central tree and that of the central component is discussed in terms of a regression function.

Keywords

RANDOM GRAPHSLIMITING DISTRIBUTIONSREGRESSION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 622 - 636
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Partial financial support for this research was obtained from the Swedish Council for the Humanities and Social Sciences, and from the Committee of Sciences, Bulgarian Council of Ministers, Contract No. 60.

References

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