The myth of equidistribution for high-dimensional simulation

TL;DR

This paper critically examines the concept of equidistribution in high-dimensional pseudo-random number generators, questioning its effectiveness as a measure of RNG quality and highlighting its limitations.

Contribution

It introduces a formal definition of (d,w)-equidistribution and argues that this property may not be a suitable criterion for evaluating RNG performance.

Findings

(d,w)-equidistribution is not always desirable for RNGs

Some RNGs outperform others despite differences in equidistribution

The paper challenges the traditional emphasis on equidistribution as a key quality metric

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.