Physics – Mathematical Physics
Scientific paper
2002-01-22
Journal of Physics A: Mathematical and General; Vol 35; No 31; 9 August 2002; Page 6557-6570
Physics
Mathematical Physics
Scientific paper
10.1088/0305-4470/35/31/303
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to be calculated for a spherical (n)-ball having an arbitrary volume density, and reproduces the well-known results for the case of uniform density. The results find applications in stochastic geometry, computational science, molecular biological systems, statistical physics, astrophysics, condensed matter physics, nuclear physics, and elementary particle physics. As one application of these results, we propose a new statistical method obtained from our formalism to study random number generators in (n)-dimensions used in Monte Carlo simulations.
Fischbach Ephraim
Tu Shu-Ju
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