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yes, this normalization will produce a uniform distribution in ${\rm SU}(N)$, however, it might be more efficient to generate directly random matrices with unit determinant (you'll need one fewer para …

there is a mathematics reason to distinguish bulk from edge, as mentioned in Ofer Zeitouni's answer, and there is a physics reason: in a physical system with an excitation gap, for example, a supercon …

This is a special case of the more general problem solved in On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices (2015). If all the $\alpha_i$'s are the same, the two dist …

upper and lower bounds for the expectation of $\log\det W$ --- with complex matrix elements, but I presume readily generalized to real matrix elements --- have been derived in On the log-determinant o …

this is a limit of a more general result by Majumdar and company, How many eigenvalues of a Gaussian random matrix are positive? (2010), see also their earlier papers from 2006 and 2008. The coeffici …

the classic example is Dyson's circular ensemble of random unitary matrices (distributed uniformly with respect to the Haar measure); in the limit of large matrix size the correlation function of the …

I assume the matrices $U_1$ and $U_2$ are independently uniformly distributed in the unitary group. The product $V=U_1^HU_2$ is then itself uniformly distributed in the unitary group. The distribution …

Real eigenvalues of non-Gaussian random matrices and their products finds that the probability that all eigenvalues are real is larger for distributions with large weight at the origin and that decay …

The solution was obtained already by Marchkenko and Pastur, in terms of the Cauchy transform $g(z)$ of the spectral density of $D+XX^{\rm T}$, see for example equations 2 + 3 of Spectrum of deformed r …

The $\sqrt{n}$ factors can be absorbed in the $X$ matrices, I can omit them. Consider a Hermitian matrix $X$ and a Hermitian perturbation $\delta X$. Then, for $f:\mathbb{R}\rightarrow\mathbb{R}$ one …

You ask for the average of the singular values of the Wishart matrix. I'm pretty sure there is no closed form expression valid for any $n$. If instead you would ask for the average of the square of th …

Indeed, if $A$ is non-Hermitian you cannot use the inverse $(A-z)^{-1}$ to study eigenvalues near a complex number $z$. To apply resolvent techniques to a non-Hermitian matrix $A$ you need to first sy …

After a cyclic permutation of the trace, the expression you need is $$Y=\text{tr}\left\{\mathbf{A}^HE(\mathbf{C}^H \begin{bmatrix} \mathbf{0}_{M\times M} & \mathbf{0}_{M\times N} \\ \mathbf{0}_{N\tim …

For a non-asymptotic result, you could just use the exact distribution of $s^2_{\rm max}$ given in Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices... (Marco Chiani …

this is not an answer to the question "what matrix model produces the eigenvalue distribution (2)", but it does explain why (2) cannot be an extrapolation between the $\beta$-Ginibre ensembles. The e …