Random and Quasi-Random Point Sets

Volume 138 of the series Lecture Notes in Statistics pp 49-108

On the Assessment of Random and Quasi-Random Point Sets

  • Peter HellekalekAffiliated withInstitut für Mathematik, Universität Salzburg

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The Monte Carlo and the quasi-Monte Carlo method are two of the most important techniques to solve multidimensional problems. In both cases, we employ deterministic algorithms to generate finite point sets in high dimensions. The quality of the equidistribution of these point sets may have a decisive influence on our numerical results. In this contribution, we will discuss the main concepts to assess equidistribution. In particular, we will present a new interpretation of the well-known spectral test.