A new formalism for geometric probability and its applications to physics

We present a new mathematical formalism for analytically obtaining the probability density function, Pn(s), of the random distance s separated by two random points distributed in a geometric object defined in n-dimensional Euclidean space. The formalism allows us to calculate Pn( s) for a spherical geometric object in n dimensions having an arbitrary non-uniform density, and reproduces the well-known results for the case of uniform density. The results find applications in elementary particle physics, statistical physics, computational science, molecular biology, geostatistics, and stochastic geometry