• 대한수학회지
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• 제35권3호
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.