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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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 annihilation.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 27, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1559700463

Digital Object Identifier
doi:10.1214/19-ECP238

Mathematical Reviews number (MathSciNet)
MR3962477

Zentralblatt MATH identifier
07068651

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

Keywords
ballistic annihilation particle system statistical physics

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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