Electronic Communications in Probability

The bullet problem with discrete speeds

Brittany Dygert, Christoph Kinzel, Matthew Junge, Annie Raymond, Erik Slivken, and Jennifer Zhu

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

ballistic annihilation particle system statistical physics

Creative Commons Attribution 4.0 International License.


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

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