Pseudo-random number generators are a critical component of many computational techniques including algorithms based on Monte Carlo methods. The emergence of parallel computers, particularly MIMD systems capable of many independent calculations, requires the development of parallel pseudo-random number generators if their range of applicability is to reach its full potential. This research will extend and generalize previous analytical results which represent generators for parallel processors. In parallel applications the correlations between generators on different processors are as important as correlations within a single sequential generator. Promising generators will be tested in an actual MIMD environment within a Monte Carlo calculation that solves the electronic structure Schrodinger equation for small clusters of helium atoms; however, effective generators will be useful in any parallel Monte Carlo calculation.
