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Habilitation à diriger des recherches

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.
Keywords : Random graphs
Document type :
Habilitation à diriger des recherches
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Contributor : Dieter Mitsche Connect in order to contact the contributor
Submitted on : Tuesday, March 22, 2016 - 1:16:19 PM
Last modification on : Saturday, June 25, 2022 - 11:18:57 PM
Long-term archiving on: : Sunday, November 13, 2016 - 11:04:48 PM


  • HAL Id : tel-01291970, version 1



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



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