## Electronic Communications in Probability

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

### Note on a one-dimensional system of annihilating particles

Vladas Sidoravicius and Laurent Tournier

#### 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