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Article Dans Une Revue Stochastic Processes and their Applications Année : 2015

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

Résumé

In this article, we study a branching random walk evolving in a (macroscopically) time-inhomogeneous environment. We compute the first two orders of the asymptotic of the maximal displacement. The ballistic first order is given by the solution of an optimization problem, while the second term is of order $n^{1/3}$. This result partially answers a conjecture of Fang and Zeitouni. Additionally, we obtain an asymptotic for the so-called consistent maximal displacement of the process, which also is of order $n^{1/3}$.
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Dates et versions

hal-00874541 , version 1 (27-05-2016)
hal-00874541 , version 2 (18-05-2019)
hal-00874541 , version 3 (17-11-2022)

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Bastien Mallein. Maximal displacement of a branching random walk in time-inhomogeneous environment. Stochastic Processes and their Applications, 2015, 125 (10), pp.3958-4019. ⟨10.1016/j.spa.2015.05.011⟩. ⟨hal-00874541v1⟩

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