  Considering a critical branching random walk on the real line. In a recent
paper, Aidekon [3] developed a powerful method to obtain the convergence in law
of its minimum after a log-factor normalization. By an adaptation of this
method, we show that the point process formed by the branching random walk and
its minimum converge in law to a Poisson point process colored by a certain
point process. This result, confirming a conjecture of Brunet and Derrida [10],
can be viewed as a discrete analog of the corresponding results for the
branching brownian motion, previously established by Arguin et al. [5] [6] and
Aidekon et al. [2].
