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On a Daley-Kendall model of random rumours

Published online by Cambridge University Press:  14 July 2016

B. Pittel
B. Pittel*
Affiliation:
The Ohio State University
*
∗Postal address: Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA.
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Abstract

Suppose that a certain population consists of N individuals. One member initially learns a rumour from an outside source, and starts telling it to other members, who continue spreading the information. A knower becomes inactive once he encounters somebody already informed. Daley and Kendall, who initiated the study of this model, conjectured that the number of eventual knowers is asymptotically normal with mean and variance linear in N. Our purpose is to confirm this conjecture.

Keywords

SPREAD OF RUMOURSMARKOV PROCESSHARMONIC FUNCTIONSLIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 14 - 27
Copyright
Copyright © Applied Probability Trust 1990 

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References

[1] Von Bahr, B. and Martin-Löf, A. (1980) Threshold limit theorems for some epidemic processes. Adv. Appl. Prob. 12, 319–349.Google Scholar
[2] Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases, and its Applications, 2nd ed. Griffin, London.Google Scholar
[3] Barbour, A. D. (1972) The principle of the diffusion of arbitrary constants. J. Appl. Prob. 9, 519–541.CrossRefGoogle Scholar
[4] Barbour, A. D. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 21–39.Google Scholar
[5] Daley, D. and Kendall, D. G. (1965) Stochastic rumours. J. Inst. Math. Appl. 1, 42–55.Google Scholar
[6] Green, R. F. (1980) The cannibals' urn. (Unpublished.) Google Scholar
[7] Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar
[8] Nagaev, A. V. and Startsev, A. N. (1970) The asymptotic analysis of a stochastic model of an epidemic. Theor. Prob. Appl. 15, 98–107.Google Scholar
[9] Pittel, B. (1987) An urn model for cannibal behavior. J. Appl. Prob. 24, 522–526.Google Scholar
[10] Scalia-Tomba, G. (1986) Asymptotic final size distribution of the multitype Reed-Frost process. J. Appl. Prob. 23, 563–584.Google Scholar
[11] Sudbury, A. (1985) The proportion of the population never hearing a rumour. J. Appl. Prob. 22, 443–446.Google Scholar
[12] Watson, R. (1988) On the size of a rumour. Stoch. Proc. Appl. 27, 141–149.Google Scholar