Minimal models of self-propelled particles with short-range volume exclusion interactions have
been shown to exhibit signatures of phase separation. Here I show that the observed interfacial sta-
bility and uctuations in motility-induced phase separations (MIPS) can be explained by modeling
the microscopic dynamics of the active particles in the interfacial region. In addition, I demon-
strate the validity of the Gibbs-Thomson relation in MIPS, which provides a functional relationship
between the size of a condensed drop and its surrounding vapor concentration. As a result, the coars-
ening dynamics of MIPS at vanishing supersaturation follows the classic Lifshitz-Slyozov scaling law
at the late stage.