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Let's say I have $M$ samples of $N\times N$ real orthogonal matrices. What statistics can I calculate to test if they could have been drawn from a distribution consistent with Haar measure over $O(N)$ …

I am just starting out on understanding random matrix theory from a background in applied mathematics. I have a very basic question about the Gaussian ensembles: why are there only three classical Gau …

For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ tha …

What is an intuitive way to understand Haar measure as defined for random matrices, say, $N\times N$ orthogonal or unitary matrices? My understanding for what Haar measure means for $U(1)$ is that it …

Consider the $N\times N$ matrix $$ M = \left(\begin{array} \\ 0 & 1 & & 0 \\ 1 & \ddots & \ddots & \\ & \ddots & \ddots & 1 \\ 0 & & 1 & 0 \\ \end{array}\right) $$ which comes from the adjacency …

I've been using the R-transform to calculate the free convolution of the eigenvalue spectra of two random matrices and I am trying to understand how it works, and in particular how it relates to noncr …