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| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed Goias, Campus Samambaia, Goiania, Go - Brazil
[2] Univ Sao Paulo, Inst Math & Stat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
[3] NYU ECNU Inst Math Sci NYU Shanghai, 3663 Zhongshan Rd North, Shanghai 200062 - Peoples R China
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 34, n. 3, p. 594-612, AUG 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We study a rumor model from a percolation theory and branching process point of view. It is defined according to the following rules: (1) at time zero, only the root (a fixed vertex of the tree) is declared informed, (2) at time n + 1, an ignorant vertex gets the information if it is, at a graph distance, at most R-v of some its ancestral vertex v, previously informed. We present relevant 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. We work with (homogeneous and non-homogeneous) Galton-Watson branching trees and spherically symmetric trees which includes homogeneous and k-periodic trees. We also present bounds for the expected size of the connected component in the subcritical case for homogeneous trees and homogeneous Galton-Watson branching trees. (AU) | |
| FAPESP's process: | 17/10555-0 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support Opportunities: | Research Projects - Thematic Grants |