Open Access
2019 The bullet problem with discrete speeds
Brittany Dygert, Christoph Kinzel, Matthew Junge, Annie Raymond, Erik Slivken, Jennifer Zhu
Electron. Commun. Probab. 24: 1-11 (2019). DOI: 10.1214/19-ECP238


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.


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Brittany Dygert. Christoph Kinzel. Matthew Junge. Annie Raymond. Erik Slivken. Jennifer Zhu. "The bullet problem with discrete speeds." Electron. Commun. Probab. 24 1 - 11, 2019.


Received: 31 May 2018; Accepted: 28 April 2019; Published: 2019
First available in Project Euclid: 5 June 2019

zbMATH: 07068651
MathSciNet: MR3962477
Digital Object Identifier: 10.1214/19-ECP238

Primary: 60K35

Keywords: ballistic annihilation , Particle system , statistical physics

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