  We introduce and investigate a new model of a finite number of particles
jumping forward on the real line. The jump lengths are independent of
everything, but the jump rate of each particle depends on the relative position
of the particle compared to the center of mass of the system. The rates are
higher for those left behind, and lower for those ahead of the center of mass,
providing an attractive interaction keeping the particles together. We prove
that in the fluid limit, as the number of particles goes to infinity, the
evolution of the system is described by a mean field equation that exhibits
traveling wave solutions. A connection to extreme value statistics is also
provided.
