Dust depleted inner disks in a large sample of transition disks through
  long-baseline ALMA observations
  Transition disks with large inner dust cavities are thought to host massive
companions. However, the disk structure inside the companion orbit and how
material flows toward an actively accreting star remain unclear. We present a
high resolution continuum study of inner disks in the cavities of 38 transition
disks. Measurements of the dust mass from archival Atacama Large
Millimeter/Submillimeter Array observations are combined with stellar
properties and spectral energy distributions to assemble a detailed picture of
the inner disk. An inner dust disk is detected in 18 of 38 disks in our sample.
Of the 14 resolved disks, 9 are significantly misaligned with the outer disk.
The near-infrared excess is uncorrelated with the mm dust mass of the inner
disk. The size-luminosity correlation known for protoplanetary disks is
recovered for the inner disks as well, consistent with radial drift. The inner
disks are depleted in dust relative to the outer disk and their dust mass is
uncorrelated with the accretion rates. This is interpreted as the result of
radial drift and trapping by planets in a low $\alpha$ ($\sim 10^{-3}$) disk,
or a failure of the $\alpha$-disk model to describe angular momentum transport
and accretion. The only disk in our sample with confirmed planets in the gap,
PDS 70, has an inner disk with a significantly larger radius and lower inferred
gas-to-dust ratio than other disks in the sample. We hypothesize that these
inner disk properties and the detection of planets are due to the gap having
only been opened recently by young, actively accreting planets.
