Re: Question about RNGs used in oct files, and multiple instances of Octave

[Francesco Potortì]

>If you are using multiple generators in parallel, if at some point the
>internal states of some generators become the same, they are now
>dependent.  They are perfectly correlated with each other.
>
>It is also possible for generators to become in step with each other,
>which is just as bad (one sequence becomes the other sequence after a
>lag).
>
>I would suggest that if you are running a stochastic program on a
>cluster of machines, and need to be sure about randomness, you get
>hardware random number generators to generate true random numbers.  If
>nothing else, they are probably faster (or could be).

From a mathematical point of view, you are right.  From a human point of
view, that depends on numbers.  The Mersenne twister used by Octavés
rand function has a period of 2^{19937}-1, which is about 1e6000.

Unless I'm mistaken, this means that if you run, say, 1e5 independent
generators each choosing a different seed and generating 1e9 random
numbers, the collision probability is around 10^-(6000-9-5-5), which is
incredibly low.

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