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$\renewcommand{\!}{\mathbf} \renewcommand{\Ai}{\operatorname{Ai}}$ One can define the Tracy-Widom distribution as the Fredholm determinant $F_2(t)=\det(\mathbf I-\mathbf A)$ where $$\mathbf A(x, y)=\...

I came across the following toy problem and was curious if there was a simple solution or counterexample. Suppose you have a distribution $p$ on $m$ random variables $X_1, \ldots, X_m$, each with ...

Let $A$ be a uniformly random $k\times k$ permutation matrix, and $A_1,\ldots, A_m$ be the $m$ independent copies of $A$. Here the uniform distribution is with respect to the $k!$ possible permutation ...