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The bullet problem with discrete speeds
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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.
Type
article
Date
2019-01
Publisher
Degree
Advisors
License
UMass Amherst Open Access Policy
License
http://creativecommons.org/licenses/by/4.0/