Abstract
Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.
Funding Statement
The work of the authors was supported in part by ISF Grants No. 1704/18 and 1985/22. The first author is a Zuckerman Postdoctoral Scholar, and this work was supported in part by the Zuckerman STEM Leadership Program. Most of this research was done while the third author was a Postdoc at the Technion–Israel Institute of Technology, supported in part by a fellowship of the Israel Council for Higher Education.
Acknowledgments
We want to thank Omer Angel, Julien Berestycki, Pascal Maillard, Michel Pain, and Eviatar Procaccia for helpful conversations. We also thank the referees for the helpful comments and suggestions. Zhenyao Sun is the corresponding author.
Citation
Clayton Barnes. Leonid Mytnik. Zhenyao Sun. "On the coming down from infinity of coalescing Brownian motions." Ann. Probab. 52 (1) 67 - 92, January 2024. https://doi.org/10.1214/23-AOP1640
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