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Article Dans Une Revue Random Structures and Algorithms Année : 2019

The combinatorics of the colliding bullets

Résumé

The finite colliding bullets problem is the following simple problem: consider a gun, whose barrel remains in a fixed direction; let (V i) 1≤i≤n be an i.i.d. family of random variables with uniform distribution on [0, 1]; shoot n bullets one after another at times 1, 2,. .. , n, where the ith bullet has speed V i. When two bullets collide, they both annihilate. We give the distribution of the number of surviving bullets, and in some generalisation of this model. While the distribution is relatively simple (and we found a number of bold claims online), our proof is surprisingly intricate and mixes combinatorial and geometric arguments; we argue that any rigorous argument must very likely be rather elaborate.
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Dates et versions

hal-02388161 , version 1 (05-02-2020)

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Jean-François Marckert, Nicolas Broutin. The combinatorics of the colliding bullets. Random Structures and Algorithms, 2019, 56 (2), pp.401-431. ⟨10.1002/rsa.20869⟩. ⟨hal-02388161⟩
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