Electronic Communications in Probability

Yet another condition for absence of collisions for competing Brownian particles

Tomoyuki Ichiba and Andrey Sarantsev

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Abstract

Consider a finite system of rank-based competing Brownian particles, where the drift and diffusion of each particle depend only on its current rank relative to other particles. We present a simple sufficient condition for absence of multiple collisions of a given order, continuing the earlier work by Bruggeman and Sarantsev (2015). Unlike in that paper, this new condition works even for infinite systems.

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 8, 7 pp.

Dates
Received: 25 August 2016
Accepted: 2 January 2017
First available in Project Euclid: 14 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1484363135

Digital Object Identifier
doi:10.1214/17-ECP41

Mathematical Reviews number (MathSciNet)
MR3607803

Zentralblatt MATH identifier
1357.60111

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60H10: Stochastic ordinary differential equations [See also 34F05] 60J65: Brownian motion [See also 58J65] 60J60: Diffusion processes [See also 58J65]

Keywords
competing Brownian particles total collision multiple collision triple collision simultaneous collision

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ichiba, Tomoyuki; Sarantsev, Andrey. Yet another condition for absence of collisions for competing Brownian particles. Electron. Commun. Probab. 22 (2017), paper no. 8, 7 pp. doi:10.1214/17-ECP41. https://projecteuclid.org/euclid.ecp/1484363135


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References

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