## The Annals of Probability

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

### Permanental vectors with nonsymmetric kernels

#### 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.

#### Article information

**Source**

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

**Dates**

Received: June 2014

Revised: January 2015

First available in Project Euclid: 26 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1485421332

**Digital Object Identifier**

doi:10.1214/15-AOP1008

**Mathematical Reviews number (MathSciNet)**

MR3601649

**Zentralblatt MATH identifier**

1375.60080

**Subjects**

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]

**Keywords**

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

#### Citation

Eisenbaum, Nathalie. Permanental vectors with nonsymmetric kernels. Ann. Probab. 45 (2017), no. 1, 210--224. doi:10.1214/15-AOP1008. https://projecteuclid.org/euclid.aop/1485421332