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. -----