Open Access
2017 On asymptotic behavior of the modified Arratia flow
Vitalii Konarovskyi
Electron. J. Probab. 22: 1-31 (2017). DOI: 10.1214/17-EJP34


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.


Download Citation

Vitalii Konarovskyi. "On asymptotic behavior of the modified Arratia flow." Electron. J. Probab. 22 1 - 31, 2017.


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

zbMATH: 1358.82013
MathSciNet: MR3622889
Digital Object Identifier: 10.1214/17-EJP34

Primary: 60K35 , 82B21
Secondary: 60D05

Keywords: asymptotic behavior , Clusters , coalescing , Interacting particle system , modified Arratia flow

Vol.22 • 2017
Back to Top