be formed by a few contact spots, whereas for ${a_{\mbox{\tiny macro}}}\gg \lambda_s$ it is expected that the contact contains a statistically meaningful number of spots. Therefore, statistical models could be accurately applied only for the later case. At the same time, it is known that the longest wavelength (of the power-law spectral decay) $\lambda_l$ determines the dispersion of results [@yastrebov2012pre; @pastewka2013pre; @yastrebov2015ijss; @rey2017hal]: therefore, to have a spatially homogeneous and statistically reproducible contact-spot distribution for all possible roughness realizations, the contact radius has to fulfil the following condition ${a_{\mbox{\tiny macro}}}\gg \lambda_l$ as well. However, this last condition should be fulfilled only for generated rough surfaces possessing discrete spectra.

Another important consideration is that in multi-asperity models it is assumed that local contact spots are located far from each other. A softer restriction would be the assumption that the contact zones associated with different asperities do not intersect. This strong limitation was partly overcame in [@afferrante2012w] by assuming that coalescing contact spots (non-convex and possibly non-simply connected) form a new effective one of a circular shape. However, this improvement requires to switch from statistical to a deterministic model. Moreover, separate asperities located on a smooth surface are inevitably separated by valleys 