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Survivors in leader election algorithms.
- Source :
-
Statistics & Probability Letters . Dec2013, Vol. 83 Issue 12, p2743-2749. 7p. - Publication Year :
- 2013
-
Abstract
- Abstract: We consider the number of survivors in a broad class of fair leader election algorithms after a number of election rounds. We give sufficient conditions for the number of survivors to converge to a product of independent identically distributed random variables. The number of terms in the product is determined by the round number considered. Each individual term in the product is a limit of a scaled random variable associated with the splitting protocol. The proof is established via convergence (to 0) of the first-order Wasserstein distance from the product limit. In a broader context, the paper is a case study of a class of stochastic recursive equations. We give two illustrative examples, one with binomial splitting protocol (for which we show that a normalized version is asymptotically Gaussian) and one with uniform splitting protocol. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01677152
- Volume :
- 83
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Statistics & Probability Letters
- Publication Type :
- Periodical
- Accession number :
- 91599856
- Full Text :
- https://doi.org/10.1016/j.spl.2013.09.011