Aspects of random graphs

Abstract : The present report aims at giving a survey of my work since the end of my PhD thesis "Spectral Methods for Reconstruction Problems". Since then I focussed on the analysis of properties of different models of random graphs as well as their connection to real-world networks. This report's goal is to capture these problems in a common framework. The very last chapter of this thesis about results in bootstrap percolation is different in the sense that the given graph is deterministic and only the decision of being active for each vertex is probabilistic; since the proof techniques resemble very much results on random graphs, we decided to include them as well. We start with an overview of the five random graph models, and with the description of bootstrap percolation corresponding to the last chapter. Some properties of these models are then analyzed in the different parts of this thesis.
Mots-clés : graphes aléatoires
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HDR
Probability [math.PR]. Université de Nice Sophia-Antipolis, 2016
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Contributeur : Dieter Mitsche <>
Soumis le : mardi 22 mars 2016 - 13:16:19
Dernière modification le : jeudi 11 janvier 2018 - 16:51:59
Document(s) archivé(s) le : dimanche 13 novembre 2016 - 23:04:48

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Dieter Mitsche. Aspects of random graphs. Probability [math.PR]. Université de Nice Sophia-Antipolis, 2016. 〈tel-01291970〉

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