Publication Date
2019
Journal or Book Title
Electronic Communications in Probability
Abstract
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.
DOI
https://doi.org/10.1214/19-ECP238
Pages
1-11
Volume
27
License
UMass Amherst Open Access Policy
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
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.
https://doi.org/10.1214/19-ECP238