The almost sure limits of the minimal position and the additive   martingale in a branching random walk
  Consider a real-valued branching random walk in the boundary case. Using the techniques developed by A\"id\'ekon and Shi [5], we give two integral tests which describe respectively the lower limits for the minimal position and the upper limits for the associated additive martingale. 
Yueyun Hu (LAGA)
math.PR