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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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https://hal.archives-ouvertes.fr/hal-01322464
Contributor : Bastien Mallein <>
Submitted on : Saturday, September 29, 2018 - 10:57:20 AM
Last modification on : Friday, June 12, 2020 - 11:02:06 AM
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Bastien Mallein, Piotr Miłoś. Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment. Stochastic Processes and their Applications, Elsevier, In press, ⟨10.1016/j.spa.2018.09.008⟩. ⟨hal-01322464v2⟩

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