  The extremal process of a branching random walk is the point measure
recording the position of particles alive at time $n$, shifted around the
expected position of the minimal position. Madaule proved that this point
measure converges, as $n \to \infty$, toward a randomly shifted, decorated
Poisson point process. In this article, we study the joint convergence of the
extremal process together with its genealogical informations. This result is
then used to describe the law of the decoration in the limiting process, as
well as to study the supercritical Gibbs measures of the branching random walk.

Probability