mean integral values (for example, mean spacing between contacting asperities, integral contact area). Such models are, in general, easier to use than deterministic but on the other hand they are inherently less precise since cannot take into account finite size of the contact area and cannot accurately resolve complex mechanical interaction between contacting spots.

In this paper we consider a contact problem between two non-conformal solids with superposed roughness. This generalization of Hertzian contact is relevant to almost all aforementioned applications since in real engineering and natural systems, the contact can be usually reduced to a contact between two smooth surfaces, whose shape is described by a two-form. Here however, we limit our attention to the contact of solids of revolution. To address this problem which was already studied using different models in different regimes [@greenwood1967elastic; @goryacheva2006mechanics; @goryacheva2013contact; @pastewka2016contact], we choose to use a deterministic multi-asperity approach, rather similar to ones elaborated in [@afferrante2012interacting; @afferrante2018elastic], which includes long-range elastic interaction between asperities. The main objective is to demonstrate capacities of the model in predicting particular features of this contact interaction for a given (deterministic) roughness. On the other hand we will explore its ability to derive statistical results, which, however, 