The Annals of Probability

Permanental vectors with nonsymmetric kernels

Nathalie Eisenbaum

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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.

Article information

Ann. Probab., Volume 45, Number 1 (2017), 210-224.

Received: June 2014
Revised: January 2015
First available in Project Euclid: 26 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 60E07: Infinitely divisible distributions; stable distributions 60E10: Characteristic functions; other transforms 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]

Gaussian vector infinite divisibility permanental vector $M$-matrix symmetrizable matrix


Eisenbaum, Nathalie. Permanental vectors with nonsymmetric kernels. Ann. Probab. 45 (2017), no. 1, 210--224. doi:10.1214/15-AOP1008.

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