Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T03:58:38.335Z Has data issue: false hasContentIssue false
  • English
  • Français

The Noisy Veto-Voter Model: A Recursive Distributional Equation on [0, 1]

Part of: Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Saul Jacka  and
Marcus Sheehan
Saul Jacka*
Affiliation:
University of Warwick
Marcus Sheehan*
Affiliation:
University of Warwick
*
∗Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
∗Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study a particular example of a recursive distributional equation (RDE) on the unit interval. We identify all invariant distributions, the corresponding ‘basins of attraction’, and address the issue of endogeny for the associated tree-indexed problem, making use of an extension of a recent result of Warren.

Keywords

Endogenyveto-voter modeldistributed error reportingbasin of attractionGalton-Watson branching process

MSC classification

Secondary: 60E05: Distributions 60E99: None of the above, but in this section 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 670 - 688
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Aldous, D. and Bandyopadhyay, A. (2005). A survey of max-type recursive distributional equations. Ann. Appl. Prob. 15, 1047–1110.Google Scholar
[2] Bandyopadhyay, A. (2006). A necessary and sufficient condition for the tail-triviality of a recursive tree process. Sankhyā 68, 1–23.Google Scholar
[3] Clifford, P. and Sudbury, A. (1973). A model for spatial conflict. Biometrika 60, 581–588.Google Scholar
[4] Cox, J. T. and Griffeath, D. (1986). Diffusive clustering in the two dimensional voter model. Ann. Prob. 14, 347–370.CrossRefGoogle Scholar
[5] Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edn. John Wiley, New York.Google Scholar
[6] Holley, R. A. and Liggett, T. M. (1975). Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Prob. 4, 643–663.Google Scholar
[7] Rüschendorf, L. (2006). On stochastic recursive equations of sum and max type. J. Appl. Prob. 43, 687–703.Google Scholar
[8] Sood, V. and Redner, S. (2005). Voter model on heterogeneous graphs. Phys. Rev. Letters 94, 178701.Google Scholar
[9] Warren, J. (2006). Dynamics and endogeny for processes indexed by trees. Stochastics 78, 327–342.Google Scholar