Physics – Computational Physics
Scientific paper
2009-09-30
Phys. Rev. E 77, 016703 (2008)
Physics
Computational Physics
18 pages, 5 figures
Scientific paper
10.1103/PhysRevE.77.016703
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a statistical estimate requires a measure of the random error in the estimate for it to be useful. Such a measure of confidence is usually provided by assuming the Central Limit Theorem to hold true. In what follows it is demonstrated that, for the most popular implementation of the Variational Monte Carlo method, the Central Limit Theorem has limited validity, or is invalid and must be replaced by a Generalised Central Limit Theorem. Estimates of the total energy and the variance of the local energy are examined in detail, and shown to exhibit uncontrolled statistical errors through an explicit derivation of the distribution of the random error. Several examples are given of estimated quantities for which the Central Limit Theorem is not valid. The approach used is generally applicable to characterising the random error of estimates, and to Quantum Monte Carlo methods beyond Variational Monte Carlo.
No associations
LandOfFree
Heavy-tailed random error in quantum Monte Carlo does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Heavy-tailed random error in quantum Monte Carlo, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heavy-tailed random error in quantum Monte Carlo will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-589177