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May 18 at 7:23 comment added lcv It may be also a question of terminology. The term resolvent was coined by David Hilbert to denote $R=(zI -A)^{-1}$ (or its opposite). In random matrices, especially to define free cumulants, the $R$ transform is related to $\langle \mathrm{Tr}(zI -A)^{-1}\rangle/N$
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