On the number of hard ball collisions

Krzysztof Burdzy, Mauricio Duarte

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are n balls of equal masses and radii 1, and at the time of a collision between any two balls the distance between any other pair of balls is greater than n−n, then the total number of collisions is bounded by n(5/2+ε)n, for any fixed ε > 0 and large n. We also show that if there is a number of collisions larger than ncn for an appropriate c > 0, then a large number of these collisions occur within a subfamily of balls that form a very tight configuration.

Original languageEnglish
Pages (from-to)373-392
Number of pages20
JournalJournal of the London Mathematical Society
Issue number1
Publication statusPublished - 30 Aug 2019


  • 37D50 (primary)
  • 70F35 (secondary)

ASJC Scopus subject areas

  • Mathematics(all)


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