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This is a follow up question on my previous question here that was on solved in the deterministic setting by Denis Serre, when the perturbation can be separated. Therefore, I decided to split the ...

We construct a non-random matrix using random variables as follows: We fix the vector $v=(1,1).$ Let $X$ be a $\mathbb R^2$-valued random variable such that $X$ is distributed according to $$d\mu(...

Let $M$ come from an ensemble of $N\times N$ matrices. The Wigner surmise is density function $p^W_0(s)=\frac{\pi}{2}se^{-\pi s^2/4}$. From a random matrix point of view, we can write $\rho^W_0(s)=\...