The cone percolation on $\bbT_d$

Authors :: Junior, Valdivino V.
Machado, Fábio P.
Zuluaga, Mauricio
Publication Year :: 2010
Abstract: We study a rumour model from a percolation theory and branching process point of view. The existence of a giant component is related to the event where the rumour 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 that defines the radius of influence of each individual.<br />Comment: 13 pages