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.

47 pages

References in corpus (2)

• Weak convergence of the localized disturbance flow to the coalescing Brownian flow
• Iterated logarithm law for sizes of clusters in Arratia flow

Cited by in corpus (3)

• Modified Massive Arratia flow and Wasserstein diffusion
• The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold
• Dean-Kawasaki equation with initial condition in the space of positive distributions