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We prove by example that the number of elastic collisions of $n$ balls of equal mass and equal size in $d$-dimensional space can be greater than $n^3/27$ for $n\geq 3$ and $d\geq 2$.
Convergence of probability measures
Patrick Billingsley · 1968
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On systems of particles with finite-range and/or repulsive interactions
L. N. Vaserstein · 1979
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On the number of collisions in a hard sphere particle system in all space
Reinhard Illner · 1989
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Finiteness of the number of collisions in a hard sphere particle system in all space. II. Arbitrary diameters and masses
Reinhard Illner · 1990
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Billiards
Valeriĭ V. Kozlov and Dmitriĭ V. Treshchëv · 1991
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Collisions in semi-dispersing billiard on Riemannian manifold
D. Burago, S. Ferleger, and A. Kononenko · 2002
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Finite-range repulsive systems of finitely many particles
Xinfu Chen and Reinhard Illner · 2004
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