Open Access
September 2017 A system of coalescing heavy diffusion particles on the real line
Vitalii Konarovskyi
Ann. Probab. 45(5): 3293-3335 (September 2017). DOI: 10.1214/16-AOP1137


We construct a modified Arratia flow with mass and energy conservation. We suppose that particles have a mass obeying the conservation law, and their diffusion is inversely proportional to the mass. Our main result asserts that such a system exists under the assumption of the uniform mass distribution on an interval at the starting moment. We introduce a stochastic integral with respect to such a flow and obtain the total local time as the density of the occupation measure for all particles.


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Vitalii Konarovskyi. "A system of coalescing heavy diffusion particles on the real line." Ann. Probab. 45 (5) 3293 - 3335, September 2017.


Received: 1 April 2015; Revised: 1 July 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812206
MathSciNet: MR3706744
Digital Object Identifier: 10.1214/16-AOP1137

Primary: 60K35 , 82B21
Secondary: 60H05 , 60J55

Keywords: Arratia flow , coalescing , Interacting particle system , Itô formula , Local time , stochastic integral with respect to flow

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 5 • September 2017
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