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arxiv: 1308.0733 · v1 · pith:MOCISQGKnew · submitted 2013-08-03 · 🧮 math.RT

The S-transform in arbitrary dimensions

classification 🧮 math.RT
keywords arbitrarydimensionstheorytransformachievedalgebraic-geometricarisingclassify
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In this note we report the solution of the problem of defining the $S$-transform in Free Probability Theory in arbitrary dimensions. This is achieved by generalising the theory and embedding it into an algebraic-geometric framework. Finally, we classify the groups arising as distributions of s-tuples of non-commutative random variables.

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