  We discuss the skeleton as a probe of the filamentary structures of a 2D
random field. It can be defined for a smooth field as the ensemble of pairs of
field lines departing from saddle points, initially aligned with the major axis
of local curvature and connecting them to local maxima. This definition is thus
non local and makes analytical predictions difficult, so we propose a local
approximation: the local skeleton is given by the set of points where the
gradient is aligned with the local curvature major axis and where the second
component of the local curvature is negative.
  We perform a statistical analysis of the length of the total local skeleton,
chosen for simplicity as the set of all points of space where the gradient is
either parallel or orthogonal to the main curvature axis. In all our numerical
experiments, which include Gaussian and various non Gaussian realizations such
as \chi^2 fields and Zel'dovich maps, the differential length is found within a
normalization factor to be very close to the probability distribution function
of the smoothed field. This is in fact explicitly demonstrated in the Gaussian
case.
  This result might be discouraging for using the skeleton as a probe of non
Gausiannity, but our analyses assume that the total length of the skeleton is a
free, adjustable parameter. This total length could in fact be used to
constrain cosmological models, in CMB maps but also in 3D galaxy catalogs,
where it estimates the total length of filaments in the Universe. Making the
link with other works, we also show how the skeleton can be used to study the
dynamics of large scale structure.
