Continuous Path Brownian Trajectories for Diffusion Monte Carlo via First- and Last-Passage Distributions

This paper provides a review of a new method of addressing problems in diffusion Monte Carlo: the Green's function first-passage method (GFFP). In particular, we address three new strands of thought and their interaction with the GFFP method: the use of angle-averaging methods to reduce vector or tensor Laplace equations to scalar Laplace equations; the use of the simulation-tabulation (ST) method to dramatically expand the range of the GFFP method; and the development of last-passage diffusion methods; these drastically improve the efficiency of diffusion Monte Carlo methods. All of these claims are addressed in detail, with specific examples.