Random-number Generators Physical Random-number Generators

R andom numbers have applications in many areas: simulation, game-playing, cryptography, statistical sampling, evaluation of multiple integrals, particletransport calculations, and computations in statistical physics, to name a few. Since each application involves slightly different criteria for judging the “worthiness” of the random numbers generated, a variety of generators have been developed, each with its own set of advantages and disadvantages. Depending on the application, three types of number sequences might prove adequate as the “random numbers.” From a purist point of view, of course, a series of numbers generated by a truly random process is most desirable. This type of sequence is called a random-number sequence, and one of the key problems is deciding whether or not the generating process is, in fact, random. A more practical sequence is the pseudo-random sequence, a series of numbers generated by a deterministic process that is intended merely to imitate a random sequence but which, of course, does not rigorously obey such things as the laws of large numbers (see page 69). Finally, a quasi-random sequence is a series of numbers that makes no pretense at being random but that has important predefine statistical properties shared with random sequences.