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$\DeclareMathOperator\Pr{P}\newcommand\cPr[2]{\Pr(#1 \mid #2)}$I have a $J \times J$ matrix: $$ M:= \begin{bmatrix} \cPr{X=1}{Y=1} & \cPr{X=2}{Y = 1} & \cdots & \cPr{X=J}{Y = 1} \\ \cPr{X=...

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 ...

Consider a random process defined on $2^{\mathcal{X}}$, i.e. all subsets of a set $\mathcal{X}$. It's well known that this process is determinantal if one can find a positive semidefinite matrix $K$, ...