Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers
Abstract
This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more accessible to physicists than the specialized mathematical literature. There are also some new results: On the practical side we give important empirical properties of large quasi-random point sets, especially the exact quadratic discrepancies; on the theoretical side, there is the exact distribution of quadratic discrepancy for random point sets.
Cite
@article{arxiv.hep-ph/9606309,
title = {Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers},
author = {Fred James and Jiri Hoogland and Ronald Kleiss},
journal= {arXiv preprint arXiv:hep-ph/9606309},
year = {2010}
}
Comments
51 pages. Full paper, including all figures also available at: ftp://ftp.nikhef.nl/pub/preprints/96-017.ps.gz Accepted for publication in Comp.Phys.Comm. Fixed some typos, corrected formula 108,figure 11 and table 2