I've seen a host of results concerning computations for $$\mathbb{E} \left[ \operatorname{tr} A^{i_1}\cdots \operatorname{tr} A^{i_j} \,\overline{\operatorname{tr} A^{k_1} \cdots \operatorname{tr} A^{k_l}} \, \right],$$ in which $A$ is a random matrix and $i_1, \ldots, i_j, k_1, \ldots, k_l$ are positive integers. The results I've for such expressions concern the cases when $A$ is a random matrix in the circular $\beta$-ensemble or a GUE matrix, for example. There are other results in a variety of different situations. What I'm interested in is the case when $A$ is a Girko matrix. That is, when $A$ has independent complex entries with mean zero and unit variance. I would think that there are results in this direction due to the independence assumption. For example, are there results for these mixed moments in the case when $A$ is a Bernoulli matrix? Any references would be greatly appreciated.
$\begingroup$
$\endgroup$
Add a comment
|