  We analyze the light curves of 413 radio sources at submillimeter wavelengths
using data from the Submillimeter Array calibrator database. The database
includes more than 20,000 observations at 1.3 and 0.8 mm that span 13 years. We
model the light curves as a damped random walk and determine a characteristic
time scale $\tau$ at which the variability amplitude saturates. For the vast
majority of sources, primarily blazars and BL Lac objects, we find only lower
limits on $\tau$. For two nearby low luminosity active galactic nuclei, M81 and
M87, however, we measure $\tau=1.6^{+3.0}_{-0.9}$ days and
$\tau=45^{+61}_{-24}$ days, respectively ($2\sigma$ errors). Including the
previously measured $\tau=0.33\pm 0.16$ days for Sgr A*, we show an
approximately linear correlation between $\tau$ and black hole mass for these
nearby LLAGN. Other LLAGN with spectra that peak in the submm are expected to
follow this correlation. These characteristic time scales are comparable to the
minimum time scale for emission processes close to an event horizon, and
suggest that the underlying physics may be independent of black hole mass,
accretion rate, and jet luminosity.
