Permanental vectors with nonsymmetric kernels

Nathalie Eisenbaum (1, 2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Keywords: MSC2010 subject classifications. 60G15 60E07 60E10 15A15 Gaussian vector infinite divisibility permanental vector M-matrix symmetrizable matrix; MSC2010 subject classifications. 60G15; 60E07; 60E10; 15A15 Gaussian vector; infinite divisibility; permanental vector; M-matrix; symmetrizable matrix

Domains: Mathematics [math]

Nathalie Eisenbaum. Permanental vectors with nonsymmetric kernels. Annals of Probability, 2017, 45, ⟨10.1214/15-aop1008⟩. ⟨hal-03897744⟩