Linear Fluctuation of Interfaces in Glauber–Kawasaki Dynamics

In this article, we find a scaling limit of the space-time mass fluctuation field of Glauber + Kawasaki particle dynamics around its hydrodynamic mean curvature interface limit. Here, the Glauber rates are scaled by K=KN K = K N (with KN↑ ∞ K N ↑ ∞ as N↑ ∞ N ↑ ∞ ), the Kawasaki rates by N² N 2 and space by 1/ N . We start the process so that the continuum interface Γ ₜ Γ t formed, between ‘high’ ρ ₊ ρ + and ‘low’ ρ ₋ ρ - density regions, is stationary that is, Γ ₜ Γ t is ‘flat’. When the Glauber rates are balanced on Tᵈ T d , the interface Γ ₜ=Γ =: v₁=0\ Γ t = Γ = { v : v 1 = 0 } is immobile and the hydrodynamic limit is given by ρ (t,v) = ρ ₊ ρ ( t , v ) = ρ + for v₁∈ (0,1/2) v 1 ∈ ( 0 , 1 / 2 ) and ρ (t,v)= ρ ₋ ρ