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A pair of flat parallel surfaces, each freely diffusing along the directionof their separation, will eventually come into contact. If the shapes of thesesurfaces also fluctuate, then contact will occur when their centers of massremain separated by a nonzero distance $\ell$. Here we examine the statisticsof $\ell$ at the time of first contact for surfaces that evolve in timeaccording to the Edwards-Wilkinson equation. We present a general approach tocalculate its probability distribution and determine how its most likely value$\ell^*$ depends on the surfaces' lateral size $L$. We are motivated by aninterest in the motion of interfaces between two phases at conditions ofthermodynamic coexistence, and in particular the annihilation of domain wallpairs under periodic boundary conditions. Computer simulations of this scenarioverify the predicted scaling behavior in two and three dimensions. In thelatter case, slow growth where $\ell^\ast$ is an algebraic function of $\log L$implies that slab-shaped domains remain topologically intact until $\ell$becomes very small, contradicting expectations from equilibrium thermodynamics.

On the weak scaling of the contact distance between two fluctuating interfaces with system size