  Consider the boundary case in a one-dimensional super-critical branching
random walk. It is known that upon the survival of the system, the minimal
position after $n$ steps behaves in probability like ${3\over 2} \log n$ when
$n\to \infty$. We give a simple and self-contained proof of this result, based
exclusively on elementary properties of sums of i.i.d. real-valued random
variables.
