التفاصيل البيبلوغرافية
| العنوان: |
Proved Random Numbers Obtained from Hardware Devices. |
| المؤلفون: |
Blacher, René1 (AUTHOR) rene.blacher@aliceadsl.fr |
| المصدر: |
Communications in Statistics: Simulation & Computation. May2014, Vol. 43 Issue 5, p1020-1035. 16p. |
| مصطلحات موضوعية: |
*PROBABILITY theory, RANDOM numbers, MATHEMATICAL proofs, MATHEMATICAL sequences, LIPSCHITZ spaces, GEOMETRIC congruences, FIBONACCI sequence |
| مستخلص: |
In a previous paper, we have showed how to obtain sequences of number proved random. With this aim, we used sequences of noisesynsuch that the conditional probabilities have Lipschitz coefficients not too large. We transformed them using Fibonacci congruences. Then, we obtained sequencesxnwhich admit the IID model for correct model. This method consisted to value the work of Marsaglia in order to build his CD-ROM. But we did not use Rap Music (as Marsaglia), but texts files. This method also uses an extractor and at the same time the notion of correct models. In this paper, we apply this method to numbers provided by machines or chips. Unfortunately, it is less sure than they have Lipschtiz coefficient not too large. But we can solve this problem: it suffices to use the Central Limit Theorem. We do it modulo 1. In this case, we use a new limit theorem, the XOR Limit theorem : asymptotic distribution of sum of random vectors modulo 1 are asymptotically independent. Then Lipschtiz coefficient of associated sequences are not too large and we can obtain IID sequences by using Fibonacci congruences. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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