Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 27, 11 pp.
The bullet problem with discrete speeds
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 annihilation.
Electron. Commun. Probab., Volume 24 (2019), paper no. 27, 11 pp.
Received: 31 May 2018
Accepted: 28 April 2019
First available in Project Euclid: 5 June 2019
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Dygert, Brittany; Kinzel, Christoph; Junge, Matthew; Raymond, Annie; Slivken, Erik; Zhu, Jennifer. The bullet problem with discrete speeds. Electron. Commun. Probab. 24 (2019), paper no. 27, 11 pp. doi:10.1214/19-ECP238. https://projecteuclid.org/euclid.ecp/1559700463