Mean maps for cosmic web structures in cosmological initial conditions
  Halos, filaments, sheets and voids in the cosmic web can be defined in terms
of the eigenvalues of the smoothed shear tensor and a threshold $\lambda_{\rm
th}$. Using analytic methods, we construct mean maps centered on these types of
structures for Gaussian random fields corresponding to cosmological initial
conditions. Each map also requires a choice of shear at the origin; we consider
three possibilities. We find characteristic sizes, shapes and other properties
of the central objects in these mean maps and explore how these properties
change with varying the threshold and smoothing scale, i.e. varying the
separation of the cosmic web into different kinds of components. The mean maps
become increasingly complex as the threshold $\lambda_{\rm th}$ decreases to
zero. We also describe scatter around these mean maps, subtleties which can
arise in their construction, and some comparisons between halos in the maps and
collapsed halos at final times.
