## Brazilian Journal of Probability and Statistics

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 17 July 2014

https://projecteuclid.org/euclid.bjps/1405603507

Digital Object Identifier
doi:10.1214/12-BJPS212

Mathematical Reviews number (MathSciNet)
MR3263053

Zentralblatt MATH identifier
1310.60139

#### Citation

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. https://projecteuclid.org/euclid.bjps/1405603507

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