Random right eigenvalues of Gaussian quaternionic matrices

Florent Benaych-Georges (1, 2) , Francois Chapon (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on more general Gaussian quaternionic random matrix models are also made.

Mots clés: Random matrices; quaternions

Domaines: Probabilités [math.PR]

Florent Benaych-Georges, Francois Chapon. Random right eigenvalues of Gaussian quaternionic matrices. 2011. ⟨hal-00587958v1⟩