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A New Geometric Probability Technique for an N-dimensional Sphere and Its Applications to Physics

Shu-Ju Tu·Ephraim Fischbach
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Abstract

A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to be calculated for a sphere having an arbitrary density distribution, and reproduces the well-known results for the case of a sphere with uniform density. The results find applications in stochastic geometry, probability distribution theory, astrophysics, nuclear physics, and elementary particle physics.

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Shu-Ju Tu, Ephraim Fischbach. 2001-05-07. A New Geometric Probability Technique for an N-dimensional Sphere and Its Applications to Physics. https://arxiv.org/abs/math-ph/0004021

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