A popular model for describing random surfaces (or interfaces between different materials or different phases of the same material, e.g. water and oil or liquid and gas) uses a Gaussian field indexed by points in a two dimensional lattice. In such models, important questions pertain to the roughness of the boundary and to the height of largest peaks.
In a series of works, Weizmann Institute researchers, in collaboration with others, introduced novel methods and managed to describe the correct asymptotics for the height of the largest peaks, and for the structure of the collection of large peaks. In spite of the considerable roughness of the interface (which increases with the size of the sample considered), the maximum height achieved exhibits remarkable tameness; in particular, its fluctuations do not increase with the size of the sample.