Random Matrix - Generalisations

Generalisations

Wigner matrices are random Hermitian matrices such that the entries

above the main diagonal are independent random variables with zero mean, and

have identical second moments.

Invariant matrix ensembles are random Hermitian matrices with density on the space of real symmetric/ Hermitian/ quaternionic Hermitian matrices, which is of the form where the function V is called the potential.

The Gaussian ensembles are the only common special cases of these two classes of random matrices.