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Theory of Stochastic Processes, 2020, Volume 25(41), Issue 2, Pages 74–80 (Mi thsp319)  
On number of particles in coalescing-fragmentating Wasserstein dynamics

Vitalii V. Konarovskyiabc

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
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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.
Funding agency Grant number
National Research Foundation of Ukraine 2020.02/0303
The work is supported by the Grant “Leading and Young Scientists Research Support” No. 2020.02/0303.
Document Type: Article
MSC: Primary 60K35, 60H05; Secondary 60H05, 60G44
Language: English
Citation: Vitalii V. Konarovskyi, “On number of particles in coalescing-fragmentating Wasserstein dynamics”, Theory Stoch. Process., 25(41):2 (2020), 74–80
Citation in format AMSBIB
\Bibitem{Kon20}
\by Vitalii~V.~Konarovskyi
\paper On number of particles in coalescing-fragmentating Wasserstein dynamics
\jour Theory Stoch. Process.
\yr 2020
\vol 25(41)
\issue 2
\pages 74--80
\mathnet{http://mi.mathnet.ru/thsp319}
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