  Debris disks are scaled-up analogs of the Kuiper Belt in which dust is
generated by collisions between planetesimals. In the "collisional cascade"
model of debris disks, dust lost to radiation pressure and winds is constantly
replenished by grinding collisions between planetesimals. The model assumes
that collisions are destructive and involve large velocities; this assumption
has not been tested beyond our Solar System. We present 0"25 ($\approx$2.4 au)
resolution observations of the $\lambda$ = 450 $\mu$m dust continuum emission
from the debris disk around the nearby M dwarf AU Microscopii with the Atacama
Large Millimeter/submillimeter Array. We use parametric models to describe the
disk structure, and an MCMC algorithm to explore the posterior distributions of
the model parameters; we fit the structure of the disk to both our data and
archival $\lambda = 1.3$ mm data (Daley et al. 2019), from which we obtain two
aspect ratio measurements at 1.3 mm ($h_{1300}$ = 0.025$^{+0.008}_{-0.002}$)
and at 450 $\mu$m ($h_{450}$ = 0.019$^{+0.006}_{-0.001}$), as well as the grain
size distribution index $q =$ 3.03 $\pm$ 0.02. Contextualizing our aspect ratio
measurements within the modeling framework laid out in Pan & Schlichting
(2012), we derive a power law index of velocity dispersion as a function of
grain size $p = 0.28 \pm 0.06$ for the AU Mic debris disk. This result implies
that smaller bodies are more easily disrupted than larger bodies by collisions,
which is inconsistent with the strength regime usually assumed for such small
bodies. Possible explanations for this discrepancy are discussed.
