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Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers

Fred James·Jiri Hoogland·Ronald Kleiss
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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.

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Fred James, Jiri Hoogland, Ronald Kleiss. 1996-08-16. Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers. https://doi.org/10.1016/s0010-4655(96)00108-7

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