We write $R_n$ for the minimal position attained after time $n$ by a branching random walk in the boundary case. In this article, we prove that $R_n - \frac{1}{2} \log n$ converges in law toward a shifted Gumbel distribution.
A necessary and sufficient condition for the non-trivial limit of the derivative martingale in a branching random walk
The almost sure limits of the minimal position and the additive martingale in a branching random walk
Weak convergence for the minimal position in a branching random walk: a simple proof
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