• Corpus ID: 7210377

Crowding of Brownian spheres

@article{Burdzy2010CrowdingOB,
  title={Crowding of Brownian spheres},
  author={Krzysztof Burdzy and Soumik Pal and Jason Swanson},
  journal={arXiv: Probability},
  year={2010}
}
We study two models consisting of reflecting one-dimensional Brownian "particles" of positive radius. We show that the stationary empirical distributions for the particle systems do not converge to the harmonic function for the generator of the individual particle process, unlike in the case when the particles are infinitely small. 

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First consider two particles diffusing on the same line, with positions at time t given by y 1(t) and y2 (t) respectively. We suppose that they cannot pass one another, so that if initially y 1(0) <