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January 2017 Permanental vectors with nonsymmetric kernels
Nathalie Eisenbaum
Ann. Probab. 45(1): 210-224 (January 2017). DOI: 10.1214/15-AOP1008

Abstract

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.

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Nathalie Eisenbaum. "Permanental vectors with nonsymmetric kernels." Ann. Probab. 45 (1) 210 - 224, January 2017. https://doi.org/10.1214/15-AOP1008

Information

Received: 1 June 2014; Revised: 1 January 2015; Published: January 2017
First available in Project Euclid: 26 January 2017

zbMATH: 1375.60080
MathSciNet: MR3601649
Digital Object Identifier: 10.1214/15-AOP1008

Subjects:
Primary: 15A15 , 60E07 , 60E10 , 60G15

Keywords: $M$-matrix , Gaussian vector , Infinite divisibility , permanental vector , symmetrizable matrix

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 1 • January 2017
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