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Marches aléatoires avec branchement et absorption

Abstract : We study unidimensional branching random walk with an absorbing barrier that kills the individuals that cross it before they reproduce. We use probabilistic methods and obtain results that provide information on the trajectories of branching random walks without absorption. In the case of a barrier set at the origin, we estimate the extinction rate in the critical and subcritical cases. Then we refine the study of the critical case by considering a second order barrier. We determine the relevant order of the position of this barrier, which is proportional to the generation to the power 1/3, and the boundary parameter which separates the survival and the extinction cases. In the extinction case, we also estimate the survival probability and the tail of the distribution of the total progeny. The setup of the last part of this thesis is a bit different since the position of the barrier depends on the number of generation we consider. We obtain a moderate deviation result for the consistent minimal displacement of the branching random walk, which presents various regimes depending on the tail of distribution of the law of the displacements.
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https://tel.archives-ouvertes.fr/tel-00544117
Contributor : Bruno Jaffuel <>
Submitted on : Tuesday, December 7, 2010 - 11:53:10 AM
Last modification on : Wednesday, December 9, 2020 - 3:10:33 PM
Long-term archiving on: : Tuesday, March 8, 2011 - 4:10:12 AM

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  • HAL Id : tel-00544117, version 1

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Bruno Jaffuel. Marches aléatoires avec branchement et absorption. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2010. Français. ⟨tel-00544117⟩

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