  We show that holographic thermal two-sided two-point correlators take the
form of a product over quasi-normal modes (QNMs). Due to this fact, the
two-point function admits a natural dispersive representation with a positive
discontinuity at the location of QNMs. We explore the general constraints on
the structure of QNMs that follow from the operator product expansion, the
presence of the singularity inside the black hole, and the hydrodynamic
expansion of the correlator. We illustrate these constraints through concrete
examples. We suggest that the product formula for thermal correlators may hold
for more general large N chaotic systems, and we check this hypothesis in
several models.
