Reduced and Extended Weak Coupling Limit

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We give an extended review of recent work on the extended weak coupling limit. Background material on completely positive semigroups and their unitary dilations is given, as well as a particularly easy construction of `quadratic noises'.
39 pages, review article for the conference "Noncommutative harmonic analysis" in Bedlewo, Poland, 2006. v1-->v2, corrections in Section 5 and changes in notation

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