Journal of the Korean Mathematical Society (대한수학회지)
- Volume 35 Issue 3
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- Pages.675-690
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- 1998
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
A ROLE OF SINGLETONS IN QUANTUM CENTRAL LIMIT THEOREMS
- Accardi, Luigi (Graduate School of Polymathematics Nagoya University) ;
- Hashimoto, Yukihiro (Graduate School of Polymathematics Nagoya University) ;
- Obata, Nobuaki (Graduate School of Polymathematics Nagoya University)
- Published : 1998.08.01
Abstract
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.
Keywords
- quantum central limit theorems;
- singleton;
- discrete group;
- monoid;
- minimal generators;
- Haagerup state;
- free group;
- independence