Quaternionic R transform and non-Hermitian random matrices.

Using the Cayley-Dickson construction we rephrase and review the non-Hermitian diagrammatic formalism [R. A. Janik, M.

Commutative law for products of infinitely large isotropic random matrices.

Ensembles of isotropic random matrices are defined by the invariance of the probability measure under the left (and right) multiplication by an arbitrary unitary matrix. We show that the multiplication of large isotropic random matrices is spectrally commutative and self-averaging in the limit of infinite matrix size N→∞. The notion of spectral commutativity means that the eigenvalue density of a product ABC.