Linear Fluctuation of Interfaces in Glauber–Kawasaki Dynamics

Abstract

Abstract 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 $$K=K_N$$ K = K N (with $$K_N\uparrow \infty $$ K N ↑ ∞ as $$N\uparrow \infty $$ N ↑ ∞ ), the Kawasaki rates by $$N^2$$ N 2 and space by 1/ N . We start the process so that the continuum interface $$\Gamma _t$$ Γ t formed, between ‘high’ $$\rho _+$$ ρ + and ‘low’ $$\rho _-$$ ρ - density regions, is stationary that is, $$\Gamma _t$$ Γ t is ‘flat’. When the Glauber rates are balanced on $${\mathbb {T}}^d$$ T d , the interface $$\Gamma _t=\Gamma =\{v: v_1=0\}$$ Γ t = Γ = { v : v 1 = 0 } is immobile and the hydrodynamic limit is given by $$\rho (t,v) = \rho _+$$ ρ ( t , v ) = ρ + for $$v_1\in (0,1/2)$$ v 1 ∈ ( 0 , 1 / 2 ) and $$\rho (t,v)= \rho _-$$ ρ