Permanental vectors with nonsymmetric kernels. (English) Zbl 1375.60080

Eisenbaum, Nathalie

Ann. Probab. 45, No. 1, 210-224 (2017).

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.

Reviewer: Kun Soo Chang (Seoul)

MSC:

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

Keywords:

Gaussian vector; infinite divisibility; permanental vector; \(M\)-matrix; symmetrizable matrix