  Over the next ten years, the Vera C.\ Rubin Observatory (VRO) will observe
$\sim$10 million active galactic nuclei (AGN) with a regular and high cadence.
During this time, the intensities of most of these AGN will fluctuate
stochastically. Here, we explore the prospects to quantify precisely these
fluctuations with VRO measurements of AGN light curves. To do so, we suppose
that each light curve is described by a damped random walk with a given
fluctuation amplitude and correlation time. Theoretical arguments and some
current measurements suggest that the correlation timescale and fluctuation
amplitude for each AGN may be correlated with other observables. We use an
expected-information analysis to calculate the precision with which these
parameters will be inferred from the measured light curves. We find that the
measurements will be so precise as to allow the AGN to be separated into up to
$\sim 10$ different correlation-timescale bins. We then show that if the
correlation time varies as some power of the luminosity, the normalization and
power-law index of that relation will be determined to
$\mathcal{O}(10^{-4}\%)$. These results suggest that with VRO, precisely
measured variability parameters will take their place alongside spectroscopy in
the detailed characterization of individual AGN and in the study of AGN
population statistics. Analogous analyses will be enabled by other time-domain
projects, such as CMB-S4.
