## 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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