  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 stability and fluctuations 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 demonstrate 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 coarsening dynamics
of MIPS at vanishing supersaturation follows the classic Lifshitz-Slyozov
scaling law at the late stage.
