The myth of equidistribution for high-dimensional simulation

Abstract

A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. We define what it means for a RNG to be (d,w)-equidistributed, and then argue that (d,w)-equidistribution is not necessarily a desirable property.

8 pages. Based on material presented at a Workshop on High Dimensional Approximation held at the Australian National University, Canberra, 19 February 2007. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub240.html