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arXiv · 2408.07766

Collision location for hard spheres in stationary regime

Krzysztof Burdzy·Shuntao Chen
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Abstract

Consider two balls with radius $r>0$ whose centers are at a distance $2$, positioned symmetrically with respect to the origin in ${\mathbb{R}}^d$. Suppose that the initial velocities are independent standard normal vectors. When $r\to0$, the collision probability goes to 0 as $r^{d-1}$, and the asymptotic collision location distribution is a (defective) $t$-distribution. This distribution is rotationally symmetric about the origin for no apparent reason.

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Krzysztof Burdzy, Shuntao Chen. 2024-08-14. Collision location for hard spheres in stationary regime. https://arxiv.org/abs/2408.07766

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