Theory of Probability and Mathematical Statistics
Collision location for hard spheres in stationary regime
Krzysztof Burdzy and Shuntao Chen
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Abstract: Consider two balls with radius r∈(0,1) whose centers are at a distance 2, positioned symmetrically with respect to the origin in ℝd. Suppose that the initial velocities are independent standard normal vectors. We prove that when r→0, the collision probability goes to 0 as rd-1, and the asymptotic collision location distribution is a (defective) t-distribution. This distribution is rotationally symmetric about the origin for no apparent reason.
Keywords: Hard spheres, collisions
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