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Permanental vectors with nonsymmetric kernels. (English) Zbl 1375.60080

The author summarizes the contents of this paper in the abstract of the paper as follows: A permanental vector with a symmetric kernel and index \(2\) is a squared Gaussian vector. The definition of permanental vectors is a natural extension of the definition of squared Gaussian vectors to nonsymmetric kernels and to positive indexes. The only known permanental vectors either have a positive definite kernel or are infinitely divisible. Are there some others? We present a partial answer to this question.

MSC:

60G15 Gaussian processes
60E07 Infinitely divisible distributions; stable distributions
60E10 Characteristic functions; other transforms
15A15 Determinants, permanents, traces, other special matrix functions
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