Electronic Journal of Probability

Maximal displacement in a branching random walk through interfaces

Bastien Mallein

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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.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 68, 40 pp.

Accepted: 21 June 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G50: Sums of independent random variables; random walks

Branching random walk random walk time-inhomogeneous environment

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Mallein, Bastien. Maximal displacement in a branching random walk through interfaces. Electron. J. Probab. 20 (2015), paper no. 68, 40 pp. doi:10.1214/EJP.v20-2828. https://projecteuclid.org/euclid.ejp/1465067174

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