  We have used the VLA to study radio variability among a sample of 18 low
luminosity active galactic nuclei (LLAGNs), on time scales of a few hours to 10
days. The goal was to measure or limit the sizes of the LLAGN radio-emitting
regions, in order to use the size measurements as input to models of the radio
emission mechanisms in LLAGNs. We detect variability on typical time scales of
a few days, at a confidence level of 99%, in half of the target galaxies.
Either variability that is intrinsic to the radio emitting regions, or that is
caused by scintillation in the Galactic interstellar medium, is consistent with
the data. For either interpretation, the brightness temperature of the emission
is below the inverse-Compton limit for all of our LLAGNs, and has a mean value
of about 1E10 K. The variability measurements plus VLBI upper limits imply that
the typical angular size of the LLAGN radio cores at 8.5 GHz is 0.2
milliarcseconds, plus or minus a factor of two. The ~ 1E10 K brightness
temperature strongly suggests that a population of high-energy nonthermal
electrons must be present, in addition to a hypothesized thermal population in
an accretion flow, in order to produce the observed radio emission.
