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2 Introduction to Pseudorandom Numbers     continued...

The truly cautious researcher assesses different random number generators as the continuum analyst makes refinements to a grid --- better and better random number generators are employed, until the answers are independent of the random number generator. This is rarely, if ever, done in practice. Waxing philosophical, one wonders what number of Monte Carlo simulations may have been performed where the answers may in fact be incorrect, but not grossly incorrect, due to a flaw inherent in the random number generator used. Traditionally, we cavalierly accept the random number generator on the architecture of interest. Fortunately, due to the early and well publicized mistakes made using random number generators, their properties were thoroughly investigated by the mathematics community, primarily in the 1950's. Most of the random number generators in use today were designed with cognizance of past pitfalls and are adequate for almost all applications. However, we conclude this section with a firm caveat emptor!