Journal or Book Title
Electronic Communications in Probability
Bullets are fired from the origin of the positive real line, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that a bullet with the second largest speed survives with positive probability, while a bullet with the smallest speed does not. This also holds for exponential spacings between firing times. Our results imply that the middle-velocity particle survives with positive probability in a two-sided version of the bullet process with three speeds known to physicists as ballistic annihiliation.
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Dygert, Brittany; Kinzel, Christoph; Junge, Matthew; Raymond, Annie; Slivken, Erik; and Zhu, Jennifer, "The bullet problem with discrete speeds" (2019). Electronic Communications in Probability. 1294.