= Principal minor resolvent trace bound
{title2=$|N^{-1}\operatorname{Tr}G_X-N^{-1}\operatorname{Tr}G_{X^{(i)}}|\leq c/(N|\operatorname{Im}z|)$}
The <eigenvalue interlacing> of a <Hermitian matrix> and a principal minor bounds the difference of their resolvent traces by a constant times $|\operatorname{Im}z|^{-1}$. When both traces are normalized by the original dimension $N$, the bound acquires $N^{-1}$. One proof writes the difference using the interlacing counting <functions>, whose difference is at most one, and bounds the integral of $|t-z|^{-2}$ by $\pi/|\operatorname{Im}z|$. This gives the admissible absolute constant $c=\pi$.
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