  We study the onset of RMT dynamics in the mass-deformed SYK model (i.e. an
SYK model deformed by a quadratic random interaction) in terms of the strength
of the quadratic deformation. We use as chaos probes both the connected
unfolded Spectral Form Factor (SFF) as well as the Gaussian-filtered SFF, which
has been recently introduced in the literature. We show that they detect the
chaotic/integrable transition of the mass-deformed SYK model at different
values of the mass deformation: the Gaussian-filtered SFF sees the transition
for large values of the mass deformation; the connected unfolded SFF sees the
transition at small values. The latter is in qualitative agreement with the
transition as seen by the OTOCs. We argue that the chaotic/integrable
deformation affect the energy levels inhomogeneously: for small values of the
mass deformation only the low-lying states are modified while for large values
of the mass deformation also the states in the bulk of the spectrum move to the
integrable behavior.
