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Characterizations of gaussian distributions on simply connected nilpotent Lie groups and symmetric spaces.
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
For simply connected nilpotent Lie groups, we show that a probability measure is gaussian in the sense of Bernstein (for a definition thereof which in a natural way involves non-commutativity) iff it is a gaussian measure in the classical sense concentrated on an abelian subgroup. Furthermore we carry over the Skitovic-Darmois theorem to symmetric spaces of non-compact type.
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