Title: "Orderly Randomness: Quasirandom Numbers and Quasi–Monte Carlo"
Modern computing has an insatiable
appetite for randomness. Cryptography and other kinds of adversarial
computation demand “true” random numbers, which have three key
properties: They are unpredictable, uncorrelated, and unbiased. Most
other applications rely on pseudorandom numbers, which give up
unpredictability but are still uncorrelated and unbiased. A third kind
of randomness is even weaker. Quasirandom numbers are neither
unpredictable nor uncorrelated; they claim only to be unbiased. They
don’t even “look” random. Nevertheless, in some circumstances
quasirandom numbers seem to be superior to pseudorandom ones. For
example, they allow faster convergence or better error bounds in certain
Monte Carlo simulations. Although quasirandom numbers have been known
since the 1950s, some of their useful properties have been recognized
only in the past few years, and they are not yet fully understood.
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