Multiplying a Gaussian Matrix by a Gaussian Vector

Pierre-Alexandre Mattei (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We provide a new and simple characterization of the multivariate generalized Laplace distribution. In particular, this result implies that the product of a Gaussian matrix with independent and identically distributed columns by an independent isotropic Gaussian vector follows a symmetric multivariate generalized Laplace distribution.

Mots clés: Gamma distribution; Laplace distribution; Product distribution; Random matrix; Scale mixture; Variance-gamma distribution

Domaines: Probabilités [math.PR]; Théorie [stat.TH]

Pierre-Alexandre Mattei. Multiplying a Gaussian Matrix by a Gaussian Vector. Statistics and Probability Letters, 2017, ⟨10.1016/j.spl.2017.04.004⟩. ⟨hal-01462941v2⟩