Vitalii V. Konarovskyi, “On number of particles in coalescing-fragmentating Wasserstein dynamics”, Theory Stoch. Process., 2020, Volume 25(41), Issue 2,Pages <nobr>74

On number of particles in coalescing-fragmentating Wasserstein dynamics

Vitalii V. Konarovskyi^abc

^a Faculty of Mathematics, Computer Science and Natural Sciences, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
^b Institute of Mathematics, University of Leipzig, Augustusplatz 10, 04109 Leipzig, Germany
^c Institute of Mathematics of NAS of Ukraine, Tereschenkivska st. 3, 01024 Kiev, Ukraine

Abstract: We consider the system of sticky-reflected Brownian particles on the real line proposed in [4]. The model is a modification of the Howitt-Warren flow but now the diffusion rate of particles is inversely proportional to the mass which they transfer. It is known that the system consists of a finite number of distinct particles for almost all times. In this paper, we show that the system also admits an infinite number of distinct particles on a dense subset of the time interval if and only if the function responsible for the splitting of particles takes an infinite number of values.

Keywords: Sticky-reflected particle system, modified massive Arratia flow, infinite dimensional singular SDE.

MSC: Primary 60K35, 60H05; Secondary 60H05, 60G44

Language: English