Squaring VEGAS -- Multidimensional Integration Using 2D Correlations

Sammanfattning: Multidimensional integrals are used in many areas of physics; electrodynamics, quantum mechanics and statistical physics, to name a few. Many integrals can not be solved analytically, but can instead be approximated numerically. VEGAS is a Monte Carlo integration algorithm, which specializes it in approximating multidimensional integrals. By treating each integration variable independently, VEGAS only offers good approximations if the characteristic regions of the integrand's graph align with the coordinate axes. This thesis presents a modified VEGAS called VEGAS squared, which tracks possible correlations between the integration variables pairwise. When integrating Gaussian functions in two and three dimensions, for which the central parts of the graphs misalign with the coordinate axes, VEGAS squared produces a standard error by a factor of 2.5 less than what VEGAS does.