Transform of Various Random Noises in Sequences of Proved Random Numbers
Rene Blacher *
Laboratory LJK, Universite de Grenoble, France.
*Author to whom correspondence should be addressed.
Abstract
In a previous paper, we have shown how to obtain sequences of numbers proved random : these sequences can be regarded as a sample of IID sequences of random variables. By using Fibonacci congruences, we transformed sequences of noises yn such that the conditional probabilities have Lipschitz coecients not too large. Then, we obtained sequences xn which admited the IID model for correct model, i.e. Fibonacci congruences behave as extractors. This method allowed to value the CD-ROM of Marsaglia. But we did not use Rap Music (as Marsaglia), but texts les. In this paper, we show that this technique can be applied for a vast majority of possible noises. In order to prove this, we shall provide all nite sequences of random variables with a well chosen measure. Then, with a probability very close to 1, the functions of Fibonacci are very good extractors. It is therefore a very ecient method to obtain sequences proved IID from almost any sequence of noises.
Keywords: Fibonacci sequence, Random numbers, Dependence, Correct models, Higher order correlation coecients, Extractors