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Mathematics > Probability

arXiv:1309.0624 (math)
[Submitted on 3 Sep 2013 (v1), last revised 7 Oct 2013 (this version, v2)]

Title:Information Transmission under Random Emission Constraints

Authors:Francis Comets, François Delarue, René Schott
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Abstract:We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at random. Each server has a random emission capital that decreases at each emission. Quantities of interest are the number of servers that receive the information before the capital of all the informed servers is exhausted and the exhaustion time. We establish limit theorems (law of large numbers, central limit theorem and large deviation principle), as n tends to infinity, for the proportion of visited vertices before exhaustion and for the total duration. The analysis relies on a construction of the transmission procedure as a dynamical selection of successful nodes in a Galton-Watson tree with respect to the success epochs of the coupon collector problem.
Subjects: Probability (math.PR)
MSC classes: 90B31, 05C81, 60F05, 60F10, 60J20, 92D30
Cite as: arXiv:1309.0624 [math.PR]
  (or arXiv:1309.0624v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1309.0624
Journal reference: Combinator. Probab. Comp. 23 (2014) 973-1009
Related DOI: https://doi.org/10.1017/S096354831400039X

Submission history

From: Francis Comets [view email]
[v1] Tue, 3 Sep 2013 09:19:25 UTC (71 KB)
[v2] Mon, 7 Oct 2013 10:33:47 UTC (71 KB)
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