The phase structure of asymmetric ballistic annihilation
Published 2018-11-20, updated 2018-12-06Version 2
In ballistic annihilation, particles are placed throughout the real line with independent spacings and each is assigned a velocity. The particles then move at their assigned velocity and annihilate upon colliding. We develop a framework to analyze the three-velocity case with arbitrary spacings, velocities, and weights. Our main theorem establishes the existence of a phase transition for all such systems, and provides an almost complete description for where it occurs. As immediate corollaries, we obtain universal bounds on the critical region, and we give a more general proof of the recent breakthrough from Haslegrave, Sidoravicius, and Tournier for the totally symmetric case.