  When a rigid rough solid slides on a rigid rough surface, it experiences a
random motion in the direction normal to the average contact plane. Here,
through simulations of the separation at single-point contact between
self-affine topographies, we characterize the statistical and spectral
properties of this normal motion. In particular, its rms amplitude is much
smaller than that of the equivalent roughness of the two topographies, and
depends on the ratio of the slider's lateral size over a characteristic
wavelength of the topography. In addition, due to the non-linearity of the
sliding contact process, the normal motion's spectrum contains wavelengths
smaller than the smallest wavelength present in the underlying topographies. We
show that the statistical properties of the normal motion's amplitude are well
captured by a simple analytic model based on the extreme value theory
framework, extending its applicability to sliding-contact-related topics.
