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|All Authors / Contributors:||
Pierre Nolin; Wendelin Werner; Université de Paris-Sud. Faculté des Sciences d'Orsay (Essonne).
|Notes:||Thèse rédigée en anglais.
Résumé étendu en français (p. 1-10).
|Description:||1 vol. (VIII-171 p.) : ill. ; 30 cm.|
|Responsibility:||Pierre Nolin ; [sous la direction de] Wendelin Werner.|
This thesis consists of six chapters, studying various questions related to percolation near criticality in two dimensions. In chapter 1, we present in detail Kesten's results and techniques allowing to describe near-critical percolation, and we derive some new consequences. We then apply these ideas in the next chapters : we study successively a model of incipient infinite cluster (chapter 2), the geometric properties of interfaces in near-critical regime (chapter 3), the gradient percolation model (chapters 4 and 5), which is a model of inhomogeneous percolation, and finally some diffusion model (chapter 6), for which we show that a fractal geometry spontaneously arises.