  We study here the extreme statistics of Brownian particles escaping from a
cusp funnel: the fastest Brownian particles among $n$ follow an ensemble of
optimal trajectories located near the shortest path from the source to the
target. For the time of such first arrivers, we derive an asymptotic formula
that differs from the classical narrow escape and dire strait obtained for the
mean first passage time. Consequently, when particles are initially distributed
at a given distance from a cusp, the fastest do see some properties
characterizing the cusp geometry. Therefore, when many particles diffuse around
impermeable obstacles, the geometry plays a role in the time to reach a target.
In the biological context of cellular transduction with signalling molecules,
having to escape such cusp-like domains slows down fast signaling. To conclude,
generating multiple copies of the same molecule helps bypass a crowded
environment to transmit a molecular signal quickly.
