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A system of coalescing heavy diffusion particles on the real line. (English) Zbl 1386.60322

Summary: 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
60H05 Stochastic integrals
60J55 Local time and additive functionals
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