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.
"Maximal displacement in a branching random walk through interfaces." Electron. J. Probab. 20 1 - 40, 2015. https://doi.org/10.1214/EJP.v20-2828