A new formalism for geometric probability and its applications to physics
Abstract
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.
Degree
Ph.D.
Advisors
Fischbach, Purdue University.
Subject Area
Particle physics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.