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We develop a quantitative model of the self-catalyzed vapor-liquid-solid growth of GaAs nanowires, that depends on only a few a priori unknown physical parameters. The model is based on the sole consideration of the As species and incorporates all relevant mechanisms of exchange of As between the vapor, liquid, and solid phases, namely direct impingement of molecules on the droplet, their re-emission by the neighboring surfaces, evaporation from the droplet, and nucleation at the solid-liquid interface. It reproduces quantitatively all salient features of our experimental study, namely the variations of nanowire growth rate with As flux, temperature, and nanowire radius. From these optimized fits, we extract a complete set of model parameters, in particular the nucleus edge energy. We also determine quantities so far inaccessible to experiment, such as the As concentration in the droplet (about 1 …