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.Comment: Published at http://dx.doi.org/10.1214/15-AOP1008 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org