  We consider a system of annihilating particles where particles start from the
points of a Poisson process on the line, move at constant i.i.d. speeds
symmetrically distributed in {-1,0,+1} and annihilate upon collision. We prove
that particles with speed 0 vanish almost surely if and only if their initial
density is smaller than or equal to 1/4, and give an explicit formula for the
probability of survival of a stationary particle, which is in accordance with
the predictions of [Droz et al. 1995]. The present proof relies essentially on
an identity proved in a recent paper by J. Haslegrave.
