Network Reconstruction with Ambient Noise

The candidate reproduces the paper’s core derivations and conclusions: the equal-time correlator identity (Eq. (7)), its short- and long-correlation expansions (Eqs. (8)–(9)), consistent reconstruction formulas (Eqs. (10a)–(10b)), the multi-channel noise generalization (Eqs. (11a)–(11b)), and geodesic-distance identifiability under a separation condition (Eqs. (12)–(13)). The steps (diagonalization, modal filtering, recomposition) match the paper’s argument; the candidate adds routine integral details omitted in the paper’s “straightforward” calculation. A minor wording issue is the candidate’s mention of “Gaussian” noise; the paper only needs the specified second-order statistics and ergodicity over long observation windows. Otherwise, the logic, assumptions (stable fixed point, symmetric Laplacian, spatially uncorrelated exponentially correlated noise, long T), and results align closely with the paper’s statements and formulas (cf. model setup and linearization through Eq. (2)–(6) ; correlator identity and expansions, Eqs. (7)–(10) ; heterogeneous noise and geodesic-distance results, Eqs. (11)–(13) ). The paper’s next-order correction (Eq. (14)) also corroborates the candidate’s O(τ0) error in the short-τ regime .