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Let $O$ be a random orthogonal matrix (according to Haar measure) of size $n$. I found by simulations that the spectral density of $O+O^\top$ is the arcsin law rescaled to the interval $[-2,2]$. I can'...

The Anderson Model is given by the random Hamiltonian (as an operator on $l^2(\mathbb{Z}^d)$) $$ H_\omega = - \triangle + V(\omega) $$ where $V(\omega) \mid x \rangle = \omega(x) \mid x \rangle$ ...

By "spectrum of a convex body", I mean: start with a convex body $B$ in $\mathbb{R}^d$, then consider the corresponding $d \times d$ covariance matrix resulting from a uniform distribution over $B$ -- ...

Suppose that $\boldsymbol{x}\in\mathbb{R}^n$ is subgaussian random vector of variance proxy $\sigma^2$, i.e., $$\forall \boldsymbol{\alpha}\in\mathbb{R}^n: \quad \quad \mathbb{E}\left[ \exp\right(\...