  The stellar kinematics of galactic disks are key to constraining disk
formation and evolution processes. In this paper, for the first time, we
measure the stellar age-velocity dispersion correlation in the inner 20 kpc
(3.5 disk scale lengths) of M31 and show that it is dramatically different from
that in the Milky Way. We use optical Hubble Space Telescope/Advanced Camera
for Surveys photometry of 5800 individual stars from the Panchromatic Hubble
Andromeda Treasury (PHAT) survey and Keck/DEIMOS radial velocity measurements
of the same stars from the Spectroscopic and Photometric Landscape of
Andromeda's Stellar Halo (SPLASH) survey. We show that the average
line-of-sight velocity dispersion is a steadily increasing function of stellar
age exterior to R=10 kpc, increasing from 30 km/s for the young upper main
sequence stars to 90 km/s for the old red giant branch stars. This monotonic
increase implies that a continuous or recurring process contributed to the
evolution of the disk. Both the slope and normalization of the dispersion vs.
age relation are significantly larger than in the Milky Way, allowing for the
possibility that the disk of M31 has had a more violent history than the disk
of the Milky Way, more in line with cosmological predictions. We also find
evidence for an inhomogeneous distribution of stars from a second kinematical
component in addition to the dominant disk component. One of the largest and
hottest high-dispersion patches is present in all age bins, and may be the
signature of the end of the long bar.
