  The formation of planetesimals is an unsolved problem in planet formation
theory. A prominent scenario for overcoming dust growth barriers in dead zones
is the gravitational collapse of locally over-dense regions, shown to robustly
produce $\sim$100 km sized objects. Still, the conditions under which
planetesimal formation occurs remain unclear. For collapse to proceed, the
self-gravity of an overdensity must overcome stellar tidal disruption on large
scales and turbulent diffusion on small scales. Here, we relate the scales of
streaming and Kelvin-Helmholtz instability, which both regulate particle
densities on the scales of gravitational collapse, directly to planetesimal
formation. We support our analytic findings by performing 3D hydrodynamical
simulations of streaming and Kelvin-Helmholtz instability and planetesimal
formation. We find that the vertical extent of the particle mid-plane layer and
the radial width of streaming instability filaments are set by the same
characteristic length scale, thus governing the strength of turbulent diffusion
on the scales of planetesimal formation. We present and successfully test a
collapse criterion: $0.1 Q \beta \epsilon^{-1}Z^{-1} \lesssim 1$ and show that
even for Solar metallicities, planetesimals can form in dead zones of
sufficiently massive disks. For a given gas Toomre-parameter $Q$, pressure
gradient $\beta$, metallicity $Z$ and local particle enhancement $\epsilon$,
the collapse criterion also provides a range of unstable scales, instituting a
promising path for studying initial planetesimal mass distributions. Streaming
instability is not required for planetesimal collapse, but by increasing
$\epsilon$, can evolve a system to instability.
