  We consider the minimum of a super-critical branching random walk.
Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044-1079] proved the tightness
of the minimum centered around its mean value. We show that a convergence in
law holds, giving the analog of a well-known result of Bramson [Mem. Amer.
Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.
