A system of coalescing heavy diffusion particles on the real line

• Vitalii Konarovskyi ^[1]
  1. [1] Chernivtsi National University

     Chernivtsi National University

     Ucrania

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 5, 2017, págs. 3293-3335
• Idioma: inglés
• DOI: 10.1214/16-AOP1137
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• Resumen

  • 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.