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arXiv · 1610.00282

The bullet problem with discrete speeds

Brittany Dygert·Christoph Kinzel·Jennifer Zhu·Matthew Junge·Annie Raymond·Erik Slivken
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Abstract

Bullets are fired, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that the second fastest bullet survives with positive probability, while a slowest bullet does not. This also holds for exponential spacings between firing times, and for certain non-uniform measures that place less probability on the second fastest bullet. Our results provide new insights into a two-sided version of the bullet process known to physicists as ballistic annihilation.

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Brittany Dygert, Christoph Kinzel, Jennifer Zhu, Matthew Junge, Annie Raymond, Erik Slivken. 2016-10-02. The bullet problem with discrete speeds. https://arxiv.org/abs/1610.00282

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