Electronic Communications in Probability

Note on a one-dimensional system of annihilating particles

Vladas Sidoravicius and Laurent Tournier

Full-text: Open access

Abstract

We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they annihilate. We assume the law of speeds to be symmetric. We prove almost sure annihilation of positive-speed particles started from the positive half-line, and existence of a regime of survival of zero-speed particles on the full-line in the case when speeds can only take 3 values. We also state open questions.

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 59, 9 pp.

Dates
Received: 1 March 2017
Accepted: 29 August 2017
First available in Project Euclid: 18 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1508292097

Digital Object Identifier
doi:10.1214/17-ECP83

Mathematical Reviews number (MathSciNet)
MR3718709

Zentralblatt MATH identifier
06797812

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

Keywords
interacting particle system ballistic annihilation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Sidoravicius, Vladas; Tournier, Laurent. Note on a one-dimensional system of annihilating particles. Electron. Commun. Probab. 22 (2017), paper no. 59, 9 pp. doi:10.1214/17-ECP83. https://projecteuclid.org/euclid.ecp/1508292097


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