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Halos, filaments, sheets and voids in the cosmic web can be defined in termsof the eigenvalues of the smoothed shear tensor and a threshold $\lambda_{\rmth}$. Using analytic methods, we construct mean maps centered on these types ofstructures for Gaussian random fields corresponding to cosmological initialconditions. Each map also requires a choice of shear at the origin; we considerthree possibilities. We find characteristic sizes, shapes and other propertiesof the central objects in these mean maps and explore how these propertieschange with varying the threshold and smoothing scale, i.e. varying theseparation of the cosmic web into different kinds of components. The mean mapsbecome increasingly complex as the threshold $\lambda_{\rm th}$ decreases tozero. We also describe scatter around these mean maps, subtleties which canarise in their construction, and some comparisons between halos in the maps andcollapsed halos at final times.

Mean maps for cosmic web structures in cosmological initial conditions