At this scale, gravity and hydrodynamics can be neglected, and only the surface tension contribution is relevant.
Capillary wave theory (CWT) is a classic account of how thermal fluctuations distort an interface.
By performing a Fourier analysis treatment, normal modes are easily found.
This divergence is nevertheless very mild: even for displacements on the order of meters the deviation of the surface is comparable to the size of the molecules.
Moreover, the introduction of an external field removes the divergence: the action of gravity is sufficient to keep the width fluctuation on the order of one molecular diameter for areas larger than about 1 mm2 (Ref.