## The Annals of Probability

- Ann. Probab.
- Volume 45, Number 5 (2017), 3293-3335.

### A system of coalescing heavy diffusion particles on the real line

#### Abstract

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.

#### Article information

**Source**

Ann. Probab., Volume 45, Number 5 (2017), 3293-3335.

**Dates**

Received: April 2015

Revised: July 2016

First available in Project Euclid: 23 September 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1506132039

**Digital Object Identifier**

doi:10.1214/16-AOP1137

**Mathematical Reviews number (MathSciNet)**

MR3706744

**Zentralblatt MATH identifier**

06812206

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B21: Continuum models (systems of particles, etc.)

Secondary: 60H05: Stochastic integrals 60J55: Local time and additive functionals

**Keywords**

Interacting particle system Arratia flow coalescing stochastic integral with respect to flow Itô formula local time

#### Citation

Konarovskyi, Vitalii. A system of coalescing heavy diffusion particles on the real line. Ann. Probab. 45 (2017), no. 5, 3293--3335. doi:10.1214/16-AOP1137. https://projecteuclid.org/euclid.aop/1506132039