Electronic Journal of Probability

On asymptotic behavior of the modified Arratia flow

Vitalii Konarovskyi

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Abstract

We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [20]. The system is a natural generalization of the coalescing Brownian motions [3, 25]. The main difference is that diffusion particles coalesce summing their mass and changing their diffusion rate inversely proportional to the mass. First we construct the system in the case where the initial mass distribution has the moment of the order greater then two as an $L_2$-valued martingale with a suitable quadratic variation. Then we find the relationship between the asymptotic behavior of the particles and local properties of the mass distribution at the initial time.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 19, 31 pp.

Dates
Received: 18 August 2016
Accepted: 30 January 2017
First available in Project Euclid: 18 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1487386997

Digital Object Identifier
doi:10.1214/17-EJP34

Mathematical Reviews number (MathSciNet)
MR3622889

Zentralblatt MATH identifier
1358.82013

Subjects
Primary: 82B21: Continuum models (systems of particles, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
modified Arratia flow interacting particle system coalescing asymptotic behavior clusters

Rights
Creative Commons Attribution 4.0 International License.

Citation

Konarovskyi, Vitalii. On asymptotic behavior of the modified Arratia flow. Electron. J. Probab. 22 (2017), paper no. 19, 31 pp. doi:10.1214/17-EJP34. https://projecteuclid.org/euclid.ejp/1487386997


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