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Marches aléatoires en milieux aléatoires: Etude de quelques modèles multidimensionnels

Abstract : This dissertation is devoted to different models of random walks in random environments; it is made of $5$ Chapters. Chapter $1$ and $4$ are surveys of literature devoted, respectively, to i.i.d model and models where environments is given by a percolation. In Chapter $2$ we study the class of walks admitting an asymptotic direction in the case of i.i.d. model, i.e. walks such that $X_n/|X_n|$ has a deterministic limit under the annealed law. We prove that a walk belongs to this class if and only if it is transient in any directions of a non empty open set of $\mathbb{R}^d$. In Chapter $3$ we study a model of continuous time random walk in a random i.i.d. environment. More precisely, we describe how the coupling of the transition vectors and the jump rates modify the speed of the walk. Chapter $5$ is devoted to a model of walk delayed by the clusters of a site subcritical percolation. We find two distinct regimes: a ballistic one and a subballistic one taking place when the attraction is strong enough.
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Submitted on : Friday, November 14, 2008 - 2:23:46 PM
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  • HAL Id : tel-00338804, version 1


François Simenhaus. Marches aléatoires en milieux aléatoires: Etude de quelques modèles multidimensionnels. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2008. Français. ⟨tel-00338804⟩



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