On the coming down from infinity of coalescing Brownian motions

Clayton Barnes; Leonid Mytnik; Zhenyao Sun

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arXiv · 2211.15298

On the coming down from infinity of coalescing Brownian motions

Clayton Barnes·Leonid Mytnik·Zhenyao Sun

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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.

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Clayton Barnes, Leonid Mytnik, Zhenyao Sun. 2022-11-28. On the coming down from infinity of coalescing Brownian motions. https://arxiv.org/abs/2211.15298

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