(fwd) Re: Real random numbers

[Jim choate]

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From: jac at ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.physics
Subject: Re: Real random numbers
Date: 24 Jun 1994 15:56:03 -0400
Organization: Supercomputer Computations Research Institute
Lines: 39
Message-ID: <2ufdoj$h69 at ds8.scri.fsu.edu>
References: <2u69cp$46q at asterix.uni-muenster.de>
NNTP-Posting-Host: ds8.scri.fsu.edu
Keywords: real random numbers , Monte Carlo simulation

In article <2u69cp$46q at asterix.uni-muenster.de> 
hoppep at asterix.uni-muenster.de (Peter Hoppe) writes:
>
>4-bit random numbers (0,1,...,15) have been produced from
>thermal noise by a complicated method.
>Since the production is not due to a determining algorithm
>(of a pseudo random generator) these numbers are 'real random numbers'.
>So a priori there could not be any periodicity in the number series.
>The equipartition has been checked by the "chi-square-test" and the
>correlations by the "serial-test" [1]. Both equipartition and 
>correlations fulfill the theoretical expectations very good.
 
>[1] D. Knuth, The Art of Computer Programming, Vol. II,
>    Addison-Wesley, 1969 

There are much tougher tests for random numbers than these, particularly 
if they are to be used for Monte Carlo where the numbers are used as 
m-tuples.  The tests you really need to make are the ones George 
Marsaglia calls the 'monkey test' and the 'birthday test', as well 
as the m-tuples test.  The first two are generalizations of the 
well known statistics problem of the monkey typing Shakespeare and 
of coincident birthdays in a group of people.  They are tough to pass. 

The problem as I see it is that 4-bit numbers do not generate much 
variability, so you will really need m-tuples of 4-tuples of these. 
This increases the chance that long range correlations will catch 
up to you when you least want them. 

I am sure George would be interested in this, however, since they have 
been looking at ways to incorporate physical noise that is truly 
random into the very sophisticated generators like the combination 
of lagged fibonacci with congruential.  The problem is that noise 
is seldom random enough, according to talks he has given. 

-- 
 James A. Carr   <jac at scri.fsu.edu>     |   "It's never confusing though, 
      http://www.scri.fsu.edu           |  because ultimately it all fits 
 Supercomputer Computations Res. Inst.  |  -- it's just cockeyed and fits  
 Florida State, Tallahassee FL 32306    |  and is fire."  -  Norman Maclean