  The solar corona produces coronal rain, hundreds of times colder and denser
material than the surroundings. Coronal rain is known to be deeply linked to
coronal heating, but its origin, dynamics, and morphology are still not well
understood. The leading theory for its origin is thermal instability (TI)
occurring in coronal loops in a state of thermal non-equilibrium (TNE), the
TNE-TI scenario. Under steady heating conditions, TNE-TI repeats in cycles,
leading to long-period EUV intensity pulsations and periodic coronal rain. In
this study, we investigate coronal rain on the large spatial scales of an
active region (AR) and over the long temporal scales of EUV intensity
pulsations to elucidate its distribution at such scales. We conduct a
statistical study of coronal rain observed over an AR off-limb with IRIS and
SDO imaging data, spanning chromospheric to transition region (TR)
temperatures. The rain is widespread across the AR, irrespective of the loop
inclination, and with minimal variation over the 5.45-hour duration of the
observation. Most rain has a downward ($87.5\%$) trajectory; however, upward
motions ($12.5\%$) are also ubiquitous. The rain dynamics are similar over the
observed temperature range, suggesting that the TR and chromospheric emission
are co-located on average. The average clump widths and lengths are similar in
the SJI channels and wider in the AIA 304 channel. We find ubiquitous
long-period EUV intensity pulsations in the AR. Short-term periodicity is found
(16 min) linked to the rain appearance, which constitutes a challenge to
explain under the TNE-TI scenario.
