  Variability of pre-main-sequence stars observed at optical wavelengths has
been attributed tofluctuations in the mass accretion rate from the
circumstellar disk onto the forming star.Detailed models of accretion disks
suggest that young deeply embedded protostars should also exhibit variations in
their accretion rates, and that these changes can be tracked indirectly by
monitoring the response of the dust envelope at mid-IR to millimeter
wavelengths. Interferometers such as ALMA offer the resolution and sensitivity
to observe small fluctuations in brightness at the scale of the disk where
episodic accretion may be driven. In this work, we present novel methods for
comparing interferometric observations and apply them to CARMA and ALMA 1.3mm
observations of deeply embedded protostars in Serpens taken 9 years apart. We
find no brightness variation above the limits of our analysis of a factor of
$\gtrsim 50\%$, due to the limited sensitivity of the CARMA observations and
small number of sources common to both epochs. We further show that follow up
ALMA observations with a similar sample size and sensitivity may be able to
uncover variability at the level of a few percent, and discuss implications for
future work.
