Spectrum–complexity matrix-element correlations

Determine how connected correlations between microscopic spectral-density fluctuations and holographic complexity matrix elements modify the generating function and the resulting time evolution of holographic complexity, including whether they alter the characteristic pole structure or its residue.

Background

The analysis assumes that the ensemble average acts only on spectral-density correlators, while the matrix elements of the complexity generating operator are treated as universal smooth functions statistically independent of microscopic spectral fluctuations. A more complete treatment would average the product of the spectral correlator and the complexity matrix element.

The unresolved issue is whether the omitted connected mixed correlator contributes additional quantum corrections. In particular, changes to the pole structure or residue could affect the linear-growth regime and the late-time behavior derived in the paper.