Abstract
The notion of probability distributions and associated characteristic functions over a set of noncommuting variables are studied. With the provision that the marginal distributions restricted to a commuting set should give the nonnegative probability distributions over those variables we find that such generalized master distributions exist which, while incorporating implicit positivity requirements, are not themselves pointwise necessarily nonnegative. The cumulant generating functions are studied and the applicability of the Marcinkiewicz theorem explored.
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Sudarshan, E.C.G. (1991). Probability Distributions over Noncommuting Variables. In: Beckmann, M.J., Gopalan, M.N., Subramanian, R. (eds) Stochastic Processes and their Applications. Lecture Notes in Economics and Mathematical Systems, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58201-1_7
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DOI: https://doi.org/10.1007/978-3-642-58201-1_7
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