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arXiv · 1309.2621

Multiple Collisions in Systems of Competing Brownian Particles

Cameron Bruggeman·Andrey Sarantsev
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Abstract

Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. We find a sufficient condition for a.s. absence of a total collision (when all particles collide) and of other types of collisions, say of the three lowest-ranked particles. This continues the work of Ichiba, Karatzas, Shkolnikov (2013) and Sarantsev (2015).

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Cameron Bruggeman, Andrey Sarantsev. 2016-05-23. Multiple Collisions in Systems of Competing Brownian Particles. https://arxiv.org/abs/1309.2621

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