Brazilian Journal of Probability and Statistics

The cone percolation on $\mathbb{T}_{d}$

Valdivino V. Junior, Fábio P. Machado, and Mauricio Zuluaga

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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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Braz. J. Probab. Stat., Volume 28, Number 3 (2014), 367-375.

First available in Project Euclid: 17 July 2014

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Coverage of space epidemic model disk-percolation rumor model


Junior, Valdivino V.; Machado, Fábio P.; Zuluaga, Mauricio. The cone percolation on $\mathbb{T}_{d}$. Braz. J. Probab. Stat. 28 (2014), no. 3, 367--375. doi:10.1214/12-BJPS212.

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