## Electronic Journal of Probability

### Maximal displacement in a branching random walk through interfaces

Bastien Mallein

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.ejp/1465067174

Digital Object Identifier
doi:10.1214/EJP.v20-2828

Mathematical Reviews number (MathSciNet)
MR3361256

Zentralblatt MATH identifier
1321.60179

Rights

#### Citation

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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