Maximal displacement in a branching random walk through interfaces

Abstract : In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains constant. We prove that the asymptotic behaviour of the maximal displacement in this process consists of a first ballistic order, given by the solution of an optimization problem under constraints, a negative logarithmic correction, plus stochastically bounded fluctuations.
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Bastien Mallein. Maximal displacement in a branching random walk through interfaces. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2015, 20, pp.68. ⟨10.1214/EJP.v20-2828⟩. ⟨hal-01214681⟩

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