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

International audienceThis paper analyses a time-inhomogeneous model with two level of randomness. In the first step a sequence of branching law is sampled independently according to a distribution on point measures. Conditionally on the realisation of this sequence (called environment) we define a branching random walk and find the asymptotic behaviour of its maximal particle. It is of the form V n − ϕ log n + o P (log n), where V n depends on the environment that behaves as a random walk and ϕ > 0 is a constant. It turns out that the logarithmic correction ϕ is bigger than in the homogenous branching case