  Large solar flares and eruptions may influence remote regions through
perturbations in the outer-atmospheric magnetic field, leading to causally
related events outside of the primary or triggering eruptions that are referred
to as "sympathetic events." We quantify the occurrence of sympathetic events
using the full-disk observations by the Atmospheric Imaging Assembly onboard
the Solar Dynamics Observatory associated with all flares of GOES class M5 or
larger from 01 May 2010 through 31 December 2014. Using a superposed-epoch
analysis, we find an increase in the rate of flares, filament eruptions, and
substantial sprays and surges more than 20 degrees away from the primary flares
within the first four hours at a significance of 1.8 standard deviations. We
also find that the rate of distant events drops by two standard deviations, or
a factor of 1.2, when comparing intervals between 4 hours and 24 hours before
and after the start times of the primary large flares. We discuss the evidence
for the concluding hypothesis that the gradual evolution leading to the large
flare and the impulsive release of the energy in that flare both contribute to
the destabilization of magnetic configurations in distant active regions and
quiet-Sun areas. These effects appear to leave distant regions, in an ensemble
sense, in a more stable state, so that fewer energetic events happen for at
least a day following large energetic events.
