No. 969

Title:

Machine Generation of Random Numbers

Author(s):

Niki, Naoto (The Institute of Statistical Mathematics)

Key words:

Abstract:

    Random numbers generated from physical processes may have the ideal statistical properties for large scale Monte Carlo simulations, if appropriate apparatuses are used. This paper discusses principles of random number extraction, software systems and the historical development, from the mathematical and engineering point of view. It is shown that apparatuses without explicit noise source are untrustworthy, that, in the method using the number of random pulses at a fixed time interval, one bit counter should be inserted between the noise source and the cyclic counter which delivers random numbers, in order to obtain sampling triggers and cancel the bias caused by the deficiency of symmetry of electronic circuits, and that, in the method using time intervals of random length, a technique using the ``parity'' of binary digits is much efficient to correct the probable bias. The controlling software coded by the author is described as an example of parallel generation of random numbers with computing, in which buffering technique is applied.