  We propose a picture of the fluctuations in branching random walks, which
leads to predictions for the distribution of a random variable that
characterizes the position of the bulk of the particles. We also interpret the
$1/\sqrt{t}$ correction to the average position of the rightmost particle of a
branching random walk for large times $t\gg 1$, computed by Ebert and Van
Saarloos, as fluctuations on top of the mean-field approximation of this
process with a Brunet-Derrida cutoff at the tip that simulates discreteness.
Our analytical formulas successfully compare to numerical simulations of a
particular model of branching random walk.
