The cone percolation on \bbT_d

2010/11/26 by Valdivino V. Junior, Junior, Valdivino V., Fábio P. Machado +3
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1011.5691

13 pages

arxiv created 2010/11/26 · openalex publication_date 2010/11/26 · arxiv updated 2010/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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