We studied global density-of-states correlation function R () R (ω) for Lévy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov’s supersymmetry approach we calculated R () R (ω) exactly in all relevant ranges of ω. At relatively low ≤ ω ≤ Γ (with Γ ≫ Δ being the effective miniband width) we found GUE-type oscillations with period of level spacing Δ, decaying exponentially at the Thouless energy scale Eₓ₇ = /2 E T h = Δ Γ / 2 π. At high energies Eₓ₇ ω ≫ E T h our results coincide with those obtained in A. V. Lunkin and K. Tikhonov, SciPost Phys. 19, 015 (2025) via cavity equation approach. Inverse of the effective miniband width, 1/ 1 / Γ, is shown to be given by the average of the local decay times over Lévy distribution.
Safonova et al. (Mon,) studied this question.