wun2k1 - Duke University Department of Physics Physics 392...

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Duke University Department of Physics Physics 392 Fall Term 2011 WUN2K FOR LECTURE 1 These are notes summarizing the main concepts you need to understand and be able to apply. “Monte Carlo” techniques for solving problems are techniques involv- ing random numbers. These methods can be extremely powerful for handling complex or multidimensional problems. Monte Carlo techniques will typically make use of pseudo-random num- ber sequences. These are generated by algorithms that make use of a “seed” to create reproducible sequences of random-seeming numbers starting from that seed. They will tend to be periodic, but the period may be extremely large. Pseudo-random numbers may also exhibit cor- relations. Different algorithms vary greatly in quality: some produce numbers which pass quite stringent tests for randomness, whereas oth- ers will have short periods and non-negligible correlations. In general, better quality random numbers will be more expensive in terms of com- putation cycles. The quality of randomness you need will depend on
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