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Diffusions in random environments and multi-excited random walks

Abstract : This work brings together five articles concerning the study of diffusions processes in random potentials and multi-excited random walks.

In the first part of this thesis, we consider the model of the diffusion in a random potential and its discrete time analogue : the random walk in a random environment. We study, in the recurrent setting, the almost sure behavior of those processes when the driving potential is in the domain of attraction of a stable law. We also characterize the rates of growth of a transient diffusion in a spectrally negative Lévy potential.

In the second part of this thesis, we study the recent model of the multi-excited random walk. In particular, we exhibit a criterion to decide whether or not the limiting speed of the walk is zero. We also characterize, in the zero speed region, all the possible rates of transience of the walk.
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Contributor : Arvind Singh <>
Submitted on : Thursday, June 28, 2007 - 4:27:34 PM
Last modification on : Wednesday, December 9, 2020 - 3:04:55 PM
Long-term archiving on: : Monday, September 24, 2012 - 10:45:17 AM


  • HAL Id : tel-00158371, version 1


Arvind Singh. Diffusions in random environments and multi-excited random walks. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2007. English. ⟨tel-00158371⟩



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