  We study the statistical properties of the eigenvalues of the primordial
tidal and deformation tensor for random Gaussian cosmic density fields. With
the tidal and deformation tensors, Hessians of the gravitational and velocity
potential, being Gaussian, the corresponding eigenvalue fields are distinctly
non-Gaussian. Following the extension of the Doroshkevich formula for the
joined distribution of eigenvalues to two-dimensional fields, we evaluate the
two- and three-point correlation functions of the eigenvalue fields. In
addition, we assess the number densities of singular points of the eigenvalue
fields and find their corresponding two- and three-point correlation functions.
  The role of tidal forces and the resulting mass element deformation in
shaping the prominent anisotropic wall-like and filamentary components of the
cosmic web has since long been recognized based on the Zel'dovich
approximation. Less well-known is that the weblike spatial pattern is already
recognizable in the primordial tidal and deformation eigenvalue field, even
while the corresponding Gaussian density and the potential field appear merely
as a spatially incoherent and unstructured random field. Furthermore, against
the background of a full phase-space assessment of structure formation in the
Universe, the caustic skeleton theory entails a fully analytical framework for
the nonlinear evolution of the cosmic web. It describes the folding of the dark
matter sheet and the emerging caustic singularities, fully specified by the
deformation eigenvalues and eigenvectors. Finally, tidal tensor eigenvalues are
of central importance, and understanding their distribution is critical in
predicting the resulting rotation and orientation.
  The current study applies to two-dimensional Gaussian random fields and will
be generalized to a three-dimensional analysis in an upcoming study.
