{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T14:54:53Z","timestamp":1777042493558,"version":"3.51.4"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T00:00:00Z","timestamp":1578441600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T00:00:00Z","timestamp":1578441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Softw Big Sci"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This is a review of pseudorandom number generators (RNG\u2019s) of the highest quality, suitable for use in the most demanding Monte Carlo calculations. All the RNG\u2019s we recommend here are based on the Kolmogorov\u2013Anosov theory of mixing in classical mechanical systems, which guarantees under certain conditions and in certain asymptotic limits, that points on the trajectories of these systems can be used to produce random number sequences of exceptional quality. We outline this theory of mixing and establish criteria for deciding which RNG\u2019s are sufficiently good approximations to the ideal mathematical systems that guarantee highest quality. The well-known RANLUX (at highest luxury level) and its recent variant RANLUX++ are seen to meet our criteria, and some of the proposed versions of MIXMAX can be modified easily to meet the same criteria.<\/jats:p>","DOI":"10.1007\/s41781-019-0034-3","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T10:22:41Z","timestamp":1578478961000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["Review of High-Quality Random Number Generators"],"prefix":"10.1007","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2928-8493","authenticated-orcid":false,"given":"Frederick","family":"James","sequence":"first","affiliation":[]},{"given":"Lorenzo","family":"Moneta","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,8]]},"reference":[{"key":"34_CR1","volume-title":"The art of computer programming, volume 2: semi-numerical algorithms","author":"DE Knuth","year":"1998","unstructured":"Knuth DE (1998) The art of computer programming, volume 2: semi-numerical algorithms, 3rd edn. 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