Nucleation in fluids: some rigorous results

In this paper we review some recent results obtained in [F. den Hollander et al., Metastability and nucleation for conservative dynamics, EURANDOM report 99-025, J. Math. Phys. (2000), to appear] on metastability and nucleation for the two-dimensional lattice gas with Kawasaki dynamics at low temperature and low density. We also present some new results on the typical path of nucleation and discuss some open problems. The conservation of particles makes the analysis much harder than for Glauber dynamics.