On number of particles in coalescing-fragmentating Wasserstein dynamics

Vitalii Konarovskyi
Theory of Stochastic Processes
Vol.25 (41), no.2, 2020, pp.74-80
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.
DOI: https://doi.org/10.37863/tsp-2295310746-81
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