This site contains some pieces of code and a handful of plots related to my* work on Quasi Monte-Carlo error estimators. It is supposed to work as a supplement of my Ph.D. thesis, QCD and QMC, developments in perturbative Quantum Chromo-Dynamics and Quasi Monte-Carlo, published under the supervision of R.Kleiss, in the Radboud University of Nijmegen, the Netherlands.

Monte-Carlo is a method of numerical integration based on statistical sampling of the integration volume. It's probabilistic nature is a virtue that leads to a comparative advantage over other, deterministic methods, as the dimensionality of the integration problem grows.

Quasi Monte-Carlo is a variant in which the integration volume is not sampled randomly, but, instead, the points are spread uniformly (hence not independently of each other) within the integration volume.

To get an idea of what "more uniformly than random" means, see the following two-dimensional pointsets. The one on the top is a random pointset (created by an implementation of the RANLUX algorithm) whereas the one on the bottom is a quasi-random pointset (created by an implementation of the Van der Corput algorithm). Uniformity is, hereby, demonstrated by the lack of clustering: the random point-set has clusters, the quasi-random has much less. For a quantitative description of how uniform a pointset is one needs a quantity called "Diaphony". Click on the images for bigger versions