Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment

Abstract : This paper analyses a time-inhomogeneous model with two level of randomness. In the first step a sequence of branching law is sampled independently according to a distribution on point measures. Conditionally on the realisation of this sequence (called environment) we define a branching random walk and find the asymptotic behaviour of its maximal particle. It is of the form V n − ϕ log n + o P (log n), where V n depends on the environment that behaves as a random walk and ϕ > 0 is a constant. It turns out that the logarithmic correction ϕ is bigger than in the homogenous branching case.
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Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01322464
Contributeur : Bastien Mallein <>
Soumis le : vendredi 27 mai 2016 - 11:13:49
Dernière modification le : mardi 11 octobre 2016 - 15:21:02
Document(s) archivé(s) le : dimanche 28 août 2016 - 10:28:37

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  • HAL Id : hal-01322464, version 1

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INSMI | UPMC | PSL | USPC

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Bastien Mallein, Piotr Miłoś. Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment. 2015. <hal-01322464>

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