aforementioned phenomena. Mechanical models of rough contact can be divided into two main classes: deterministic and statistical models. The former models rely on direct numerical simulations of contact [@pei2005jmps; @campana2006practical; @anciaux2009ijnme; @yastrebov2011rough; @putignano2012ijss; @afferrante2012w; @bemporad2015optimization; @muser2017meeting] and take as an input the topographical data of contacting surfaces and their material properties in order to predict integral quantities such as interface stiffness, evolution and growth of true contact area and of the mean gap under increasing pressure, etc. In addition, such models allow to study the shape and spatial distribution of contacting clusters, local stress states, critical zones, etc. These models are especially important for situations when the contact area is small or when the roughness of contacting solids cannot be seen as homogeneous at the scale of contact area, for example, the rough surface can have critical defects, rare high asperities or rare third-body particles. On the contrary, the statistical models [@greenwood1966prcl; @bush1975w; @persson2001jcp; @carbone2008jmps] require only a few parameters of surface roughness (for example, root-mean squared height or surface gradient, probability density, fractal dimension) and are appropriate for situations of homogeneous roughness. These models can yield results in terms of statistical distributions (for example, pressure and tangential tractions) and 