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An Improved Upper Bound on the Number of Billiard Ball Collisions

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Abstract

We give a new upper bound \(K_+\) on the number of totally elastic collisions of n hard spheres with equal radii and equal masses in \(R^d\). Our bound satisfies \(\log K_+ \le c(d) n \log n\).

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Acknowledgements

I am grateful to Soumik Pal for very helpful advice. I thank the anonymous referees for many significant suggestions for improvement.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    Krzysztof Burdzy

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  1. Krzysztof Burdzy
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Correspondence to Krzysztof Burdzy.

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Communicated by H-T. Yau.

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Supported in part by Simons Foundation Grant 506732.

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Burdzy, K. An Improved Upper Bound on the Number of Billiard Ball Collisions. Commun. Math. Phys. 391, 107–117 (2022). https://doi.org/10.1007/s00220-021-04278-6

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  • DOI: https://doi.org/10.1007/s00220-021-04278-6

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