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 ($2sigma$ errors). Including the previously measured $tau=0.33pm 0.16$ 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.
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