A New Geometric Probability Technique for an N-dimensional Sphere and Its Applications to Physics
arXiv:math-ph/0004021
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.
REVTeX 3.1, 51 pages, 9 figures, contents rewritten, submitted to Journal of Mathematical Physics