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

Protostellar Feedback in Turbulent Fragmentation: Consequences for Stellar Clustering and Multiplicity