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Can we get that $ P(N^{2/3}(\lambda_N-\lambda_{N-1})\le c)\ge 1-\epsilon$?
Following this question: Can we apply the continuous mapping theorem for the limiting joint distribution of the Tracy-Widom law?.
We know that
$$
\lim_{N\to\infty}P(N^{2/3}(\lambda_N-2)\le s_1,\dotsc,...
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