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In a physics paper I found a very complicated Gaussian matrix model: $$ Z = \int \frac{d\mu}{(2\pi)^n} \frac{d\nu}{(2\pi)^n} \frac{ \prod_{i < j}\left[2 \sinh \frac{\mu_i - \mu_j}{2} \right]^2 \...

I'm trying to upper bound the $\epsilon$-packing number of $\Theta=\{A\in\mathbb{S}^{d}:\; a\preceq A \preceq b\}$ (where $\mathbb{S}$ are symmetric $d\times d$ matrices) for some $a\leq b$ with ...

It is known how to calculate the integral of elements of $N\times N$ Haar random unitaries using the Weingarten function: $$\int \prod_{k=1}^n U_{i_kj_k} U_{m_kr_k}^* \mathrm d U = \sum_{\sigma,\tau} \...