The bullet problem with discrete speeds
Probability
2018-05-31 v4
Abstract
Bullets are fired, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that the second fastest bullet survives with positive probability, while a slowest bullet does not. This also holds for exponential spacings between firing times, and for certain non-uniform measures that place less probability on the second fastest bullet. Our results provide new insights into a two-sided version of the bullet process known to physicists as ballistic annihilation.
Keywords
Cite
@article{arxiv.1610.00282,
title = {The bullet problem with discrete speeds},
author = {Brittany Dygert and Christoph Kinzel and Jennifer Zhu and Matthew Junge and Annie Raymond and Erik Slivken},
journal= {arXiv preprint arXiv:1610.00282},
year = {2018}
}
Comments
12 pages, 3 figures. Streamlined introduction and proofs. Simplified theorem statements. Added applications to ballistic annihilation. Updated references