Fast Diffusion Monte Carlo Sampling via Conformal Map

Abstract

In diffusion Monte Carlo methods, depending on the geometry continuous diffusion can be simulated in many ways such as walk-on-spheres (WOS), walk-on-planes (WOP), walk-on-rectangles (WOR) and so on. The diffusion ways are conformally the same satisfying the Laplace equation with the given boundary geometry. In this paper, using the WOP and the conformal map we sample the WOS diffusion and show that the indirect sampling is more efficient than the direct WOS sampling. This signifies that fast diffusion Monte Carlo sampling via conformal map can be possible.