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On a simple formula for random mappings and its applications

Published online by Cambridge University Press:  14 July 2016

Y. D. Burtin
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Abstract

A random mapping of a countable set N into itself is studied. An explicit formula is found for the probability that a subset of N will not contain cycles of the mapping. This formula is applied then for a detailed asymptotic analysis of two special mappings.

Keywords

RANDOM GRAPHRANDOM MAPPINGEPIDEMIC PROCESSATTRACTING CENTERLIMITING DISTRIBUTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 403 - 414
Copyright
Copyright © Applied Probability Trust 1980 

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References

Burtin, Y. D. (1974) On extreme metric characteristic of a random graph. I. Asymptotic estimates. Theory Prob. Appl. 19, 710–725.Google Scholar
Burtin, Y. D. (1975) On extreme metric characteristic of a random graph. II. Theory Prob. Appl. 20, 83–101.CrossRefGoogle Scholar
Gertsbakh, I. B. (1977) Epidemic processes on a random graph: Some preliminary results. J. Appl. Prob. 14, 427–438.CrossRefGoogle Scholar
Stepanov, V. E. (1971) Random mappings with a single attracting centre. Theory Prob. Appl. 16, 155–161.Google Scholar