All Questions

Let $M$ a random GOE matrix, i.e. $M=(M_{i,j})$ is a symmetric matrix and the $M_{i,j},i\leq j$ are independent centred Gaussien entries with variance 1, except on the diagonal where the variance is $...

Is there a known expression for the eigenvalue distribution of a matrix of the form $$\sum_{i=1}^n k_ia_ia_i^T$$ where $a_i \in \mathcal{R}^m$, with $n > m$, $a_i \sim \mathcal{N}(0,\Sigma)$ and $...

Given $m,n,\ell\in\Bbb N$ and $\beta\in(0,1)$ consider the uniformly picked random matrix $A\in\Bbb Z^{n\times (n+1)}$ with $0\neq|\mathsf{det}(A^\circ)|\leq m^{\frac 1\ell}$ where $A^\circ$ is the ...