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August 2014 The cone percolation on $\mathbb{T}_{d}$
Valdivino V. Junior, Fábio P. Machado, Mauricio Zuluaga
Braz. J. Probab. Stat. 28(3): 367-375 (August 2014). DOI: 10.1214/12-BJPS212

Abstract

We study a rumor model from a percolation theory and a branching process point of view. The existence of a giant component is related to the event where a rumor spreads out trough an infinite number of individuals. We present sharp lower and upper bounds for the probability of that event, according to the distribution of the random variables defining the radius of influence of each individual.

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Valdivino V. Junior. Fábio P. Machado. Mauricio Zuluaga. "The cone percolation on $\mathbb{T}_{d}$." Braz. J. Probab. Stat. 28 (3) 367 - 375, August 2014. https://doi.org/10.1214/12-BJPS212

Information

Published: August 2014
First available in Project Euclid: 17 July 2014

zbMATH: 1310.60139
MathSciNet: MR3263053
Digital Object Identifier: 10.1214/12-BJPS212

Keywords: Coverage of space , disk-percolation , Epidemic model , rumor model

Rights: Copyright © 2014 Brazilian Statistical Association

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Vol.28 • No. 3 • August 2014
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