Stochastic geometry and topology of non-Gaussian fields
  Gaussian random fields pervade all areas of science. However, it is often the
departures from Gaussianity that carry the crucial signature of the nonlinear
mechanisms at the heart of diverse phenomena, ranging from structure formation
in condensed matter and cosmology to biomedical imaging. The standard test of
non-Gaussianity is to measure higher order correlation functions. In the
present work, we take a different route. We show how geometric and topological
properties of Gaussian fields, such as the statistics of extrema, are modified
by the presence of a non-Gaussian perturbation. The resulting discrepancies
give an independent way to detect and quantify non-Gaussianities. In our
treatment, we consider both local and nonlocal mechanisms that generate
non-Gaussian fields, both statically and dynamically through nonlinear
diffusion.
