  Stars are strongly clustered on both large (~pc) and small (~binary) scales,
but there are few analytic or even semi-analytic theories for the correlation
function and multiplicity of stars. In this paper we present such a theory,
based on our recently-developed semi-analytic framework called MISFIT, which
models gravito-turbulent fragmentation, including the suppression of
fragmentation by protostellar radiation feedback. We compare the results
including feedback to a control model in which it is omitted. We show that both
classes of models robustly reproduce the stellar correlation function at >0.01
pc scales, which is well approximated by a power-law that follows generally
from scale-free physics (turbulence plus gravity) on large scales. On smaller
scales protostellar disk fragmentation becomes dominant over common core
fragmentation, leading to a steepening of the correlation function.
Multiplicity is more sensitive to feedback: we found that a model with the
protostellar heating reproduces the observed multiplicity fractions and mass
ratio distributions for both Solar and sub-Solar mass stars (in particular the
brown dwarf desert), while a model without feedback fails to do so. The model
with feedback also produces an at-formation period distribution consistent with
the one inferred from observations. However, it is unable to produce
short-range binaries below the length scale of protostellar disks. We suggest
that such close binaries are produced primarily by disk fragmentation and
further decrease their separation through orbital decay.
