Sunder Sethuraman: On derivation of mean curvature flow and fluctuations from microscopic interactions

We consider a reaction/diffusion particle system, namely `balanced' Glauber+Kawasaki models, on an n dimensional torus in which there are two preferred mass densities, a_1, a_2.  One may understand, when viewed in appropriate scales for the diffusion and reaction schemes, that a rough interface forms between the regions where the mass density is close to a_1 or a_2.  We discuss that the continuum limit is a sharp interface flow by mean curvature.  We also examine the fluctuations of mass near this forming interface in a stationary regime-when the interface is flat and not moving.  The fluctuation limits found in dimensions n=1,2 curiously involve a sense of ‘rigidity’.