# Constrained information transmission on Erdös-Rényi graphs

Abstract : We model the transmission of information of a message on the Erdös-Rény 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 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 $n\to \infty$ and $p$ is fixed, for the final proportion of informed servers.
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Cited literature [22 references]

https://hal.archives-ouvertes.fr/hal-00918904
Contributor : Francis Comets <>
Submitted on : Thursday, September 24, 2015 - 10:09:46 AM
Last modification on : Saturday, March 28, 2020 - 2:11:44 AM
Document(s) archivé(s) le : Tuesday, December 29, 2015 - 9:43:33 AM

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trans-info-rev.pdf
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### Identifiers

• HAL Id : hal-00918904, version 1
• ARXIV : 1312.3897

### Citation

Francis Comets, Christophe Gallesco, Serguei Popov, Marina Vachkovskaia. Constrained information transmission on Erdös-Rényi graphs. 2013. ⟨hal-00918904⟩

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