  Sgr A* exhibits flares in radio, millimeter and submm wavelengths with
durations of $\sim 1$ hour. Using structure function, power spectrum and
autocorrelation function analysis, we investigate the variability of Sgr A* on
time scales ranging from a few seconds to several hours and find evidence for
sub-minute time scale variability at radio wavelengths. These measurements
suggest a strong case for continuous variability from sub-minute to hourly time
scales. This short time scale variability constrains the size of the emitting
region to be less than 0.1\,AU. Assuming that the minute time scale
fluctuations of the emission at 7\,mm arise through the expansion of regions of
optically thick synchrotron-emitting plasma, this suggests the presence of
explosive, energetic expansion events at speeds close to $c$. The required rate
of mass processing and energy loss of this component are estimated to be $\ga
6\times 10^{-10} \msol$ yr$^{-1}$ and 400\,$L_\odot$ respectively. The inferred
scale length corresponding to one-minute light travel time is comparable to the
time averaged spatially resolved 0.1AU scale observed at 1.3mm emission of Sgr
A*. This steady component from Sgr A* is interpreted mainly as an ensemble
average of numerous weak and overlapping flares that are detected on short time
scales. The nature of such short time scale variable emission or quiescent
variability is not understood but could result from fluctuations in the
accretion flow of Sgr A* that feed the base of an outflow or jet.
