A random number generator doesn't become "bad" just because there are to many samples.  It depends on whether the spurious correlations are important.  In practice I find that the more common error is to model two Monte Carlo variables as independent when they really should be correlated. Brent On 3/10/2019 4:09 PM, Dan Asimov wrote:

It's not like there's some particular bad interaction between pseudo-random number generators and high-dimensional geometry.

Isn't it really that

a) one often needs many samples to get accurate estimates in the vastness of high-dimensional space,

and

b) with too many samples, a pseudorandom number generator isn't.

—Dan

Fred Lunnon écrit: -----

Where higher dimensional geometry is involved, bear in mind that even a well-designed pseudo-random number generator is only independent to some fixed precision. Once dimension x (user-demanded precision) exceeds this quantity, the randomness becomes compromised: heed the awful warning in G. Marsaglia "Random numbers fall mainly in the planes" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC285899/pdf/pnas00123-0038.pdf

This effective precision is invariably omitted from a PRNG specification, and must instead be deduced from a detailed inspection of the algorithm. -----

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