Branching processes in the phase transition of the Erdos-Renyi random graph
| Author(s): |
Comets, F.
;
Gallesco, C.
;
Popov, S.
;
Vachkovskaia, M.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Markov Processes and Related Fields; v. 22, n. 1, p. 111-138, 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
We model the transmission of information of a message on the Erdos - Renyi random graph with parameters (n, p) and limited resources. The vertices of the graph represent servers that may broadcast a message at random. Each server has a random emission capital that decreases by one at each emission. We examine two natural dynamics: in the first dynamics, an informed server performs all its attempts, then checks at each of them if the corresponding edge is open or not; in the second dynamics the informed server knows a priori who are its neighbors, and it performs all its attempts on its actual neighbors in the graph. In each case, we obtain first and second order asymptotics (law of large numbers and central limit theorem), when n -> infinity and p is fixed, for the final proportion of informed servers. (AU) | |
| FAPESP's process: | 13/10101-9 - Localization of random walks in random environment and molecular spiders |
| Grantee: | Christophe Frédéric Gallesco |
| Support type: | Regular Research Grants |
| FAPESP's process: | 09/52379-8 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support type: | Research Projects - Thematic Grants |