We studied global density-of-states correlation function $R(\omega)$ for L\'evy-Rosenzveig-Porter random matrix ensemble~\cite{BirTar_Levy-RP} in the non-ergodic extended phase. Using extension of Efetov's supersymmetry approach ~\cite{MirFyod_non_Gauss} we calculated $R(\omega)$ exactly in all relevant ranges of $\omega$. At relatively low $\omega \leq \Gamma$\, (with $\Gamma \gg \Delta$ being effective mini-band width) we found GUE-type oscillations with period of level spacing $\Delta$, decaying exponentially at the Thouless energy scale $E_{Th} = \sqrt{\Delta \Gamma/2\pi}$. At high energies $\omega \gg E_{Th}$ our results coincide with those obtained in Ref.~\cite{lunkin2024localdensitystatescorrelations} via cavity equation approach. Inverse of the effective mini-band width $1/\Gamma$ is shown to be given by the average of the local decay times over L\'evy distribution.
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