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I know that the limiting eigenvalue distribution satisfies a variational principle (see e.g. the joint work with A. Kuijlaars Large Deviations for a Non-Centered Wishart Matrix) from which you may der …

Consider a matrix $U$ from the unitary group $U_N(\mathbb{C})$ and consider the map $f:U_N(\mathbb{C})\rightarrow U_N(\mathbb{C})$ where $f(U)$ is the matrix of the eigenvectors of $U$. What is know …

The trace-class norm of $A$ is about putting the $\ell^1$ norm on the singular values of $A$, whereas the Hilbert-Schmidt norm uses $\ell^2$ instead. So your question is basically: why should we care …

Stieljes transform is about taking convolution of your signal $s(t)$ with the $\frac1 t$, so as to obtain $$ C_s(z)=\int \frac{s(t)}{z-t}dt.$$ It is of course well defined at least when $z$ is a compl …

Consider a fixed $N\times N$ positive definite symmetric matrix $A$. Assume $N=d^r$ for some $d,r\geq 1$. I wonder if one can find a closed formula for the maximizer/maximum of the function $$f(x):=\ …

I believe the relation between deterministic graphs and free probability you mentioned is not something generic. In fact, the main property of your matrix $M$ which makes connection with free probabil …

During the preparation of a general audience talk on why mathematicians use dimensions higher than three (or four) even for concrete applications, I came up with the following enjoyable observation : …