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Theses

Marches aléatoires en milieux aléatoires et phénomènes de ralentissement

Abstract : Random walks in random environments is a suitable model to describe diffusions in inhomogeneous media that have regularity properties on a macroscopic scale. The three first chapters are introductive : chapter 1 is a short general introduction, chapter 2 presents the models considered afterwards and chapter 3 is a brief overview of the results obtained. The proofs are postponed to the chapters4, 5 and 6.The content of chapter 4sheds light on limit theorems for a biased random walk on a Galton-Watson tree with leaves in the transient and sub-ballistic regime. Next, chapter 5 deals with the behaviour of the speed of a biased random walk on a percolation cluster as the percolation parameter goes to 1. An expansion of the speed in function of the percolation parameter is obtained. It can be deduced from this that the speed is increasing in $p=1$. Finally, chapter 6 tackles the problem of moderate deviations for random walks in random environments in dimension $1$.
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Alexander Fribergh. Marches aléatoires en milieux aléatoires et phénomènes de ralentissement. Mathématiques générales [math.GM]. Université Claude Bernard - Lyon I, 2009. Français. ⟨NNT : 2009LYO10078⟩. ⟨tel-00653469⟩

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