Abstract
We study a system of gravitationally interacting sticky particles. At the initial time, we have n particles, each with mass 1/n and momentum 0, independently spread on [0, 1] according to the uniform law. Due to the confining of the system, all particles merge into a single cluster after a finite time. We give the asymptotic laws of the time of the last collision and of the time of the kth collision, when n→∞. We prove also that clusters of size k appear at time ∼n −1/2(k−1). We then investigate the system at a fixed time t<1. We show that the biggest cluster has size of order logn, whereas a typical cluster is of finite size.
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Giraud, C. Clustering in a Self-Gravitating One-Dimensional Gas at Zero Temperature. Journal of Statistical Physics 105, 585–604 (2001). https://doi.org/10.1023/A:1012227809576
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DOI: https://doi.org/10.1023/A:1012227809576