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On the number of hard ball collisions
Journal of the London Mathematical Society ( IF 1.121 ) Pub Date : 2019-08-30 , DOI: 10.1112/jlms.12274
Krzysztof Burdzy; Mauricio Duarte

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 n c n for an appropriate c > 0 , then a large number of these collisions occur within a subfamily of balls that form a very tight configuration.
更新日期:2020-04-23

 

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