An improved upper bound on the number of billiard ball collisions

preprint2021arXivOpen access

Abstract

We give a new upper bound K+K_+ on the number of totally elastic collisions of nn hard spheres with equal radii and equal masses in RdR^d. Our bound satisfies log⁡K+≤c(d)nlog⁡n\log K_+ \leq c(d) n \log n.

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