  We compile and analyse long term (~10 year) submillimetre (1.3, 0.87, 0.43
mm, submm) wavelength light curves of the Galactic centre black hole,
Sagittarius A*. The 0.87 and 0.43 mm data are taken from the literature, while
the majority of the 1.3 mm light curve is from previously unpublished SMA and
CARMA data. We use Monte Carlo simulations to show that on minute to few hour
time-scales the variability is consistent with a red noise process with a 230
GHz power spectrum slope of 2.3+0.8-0.6 at 95% confidence. The light curve is
de-correlated (white noise) on very long (month to year) times. In order to
identify the transition time between red and white noise, we model the light
curves as a stochastic damped random walk process. The models allow a
quantitative estimate of this physical characteristic time-scale of 8-4+3 hours
at 230 GHz at 95% confidence, with consistent results at 345 and 690 GHz. This
corresponds to ~10 orbital times or ~1 inflow (viscous) time at R = 3 Rs, a
typical radius producing the 230 GHz emission as measured by very long baseline
interferometry and found in theoretical accretion flow and jet models. This
time-scale is significantly shorter (longer) than those measured at radio
(near-infrared, NIR) wavelengths, and is marginally inconsistent with the same
variability mechanism operating in the submm and NIR for the expected t ~ R^3/2
scaling. It is crudely consistent with the analogous time-scale inferred in
studies of quasar optical light curves after accounting for the difference in
emission radius. We find evidence that the submm variability persists at least
down to the ISCO, if not the event horizon. These results can be compared
quantitatively with similar analyses at different wavebands to test for
connections between the variability mechanisms, and with light curves from
theoretical models of accreting black holes.
