Transition disks with large inner dust cavities are thought to be carved by massive companions. How gas and dust flow inside the companion orbit supplying material to the inner disk is still not fully understood.
We present a homogeneous multi-wavelength analysis of the dust emission in a sample of transition disks. Spatially resolved measurements of continuum emission from archival Atacama Large Millimeter/Submillimeter Array are combined with centimeter observations to study the spectral index of the inner and outer disks separately. While the emission from the outer disks is consistent with thermal dust emission, most of the spectral indices estimated for the inner disks suggest that this emission is non-thermal and likely associated with an ionized jet or a disk wind. The lack of mm-dust grains in the majority of inner disks in transition disks suggests that either such dust grains have drifted quickly towards the central star, grain growth is less efficient in the inner disk, grains grow rapidly to planetesimal sizes in the inner disk, or the inner disk is not replenished from the outer disk. This will have important consequences for the presence of large grains in circumplanetary disks (CPDs) as well.