title: Stochastic geometry and topology of non-Gaussian fields.
abstract: 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.
authors.affiliation: Instituut-Lorentz for Theoretical Physics,  Leiden University, NL 2333 CA Leiden,  The Netherlands.
authors.forename: Thomas H
authors.initials: TH
authors.lastname: Beuman
authors.forename: Ari M
authors.initials: AM
authors.lastname: Turner
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Vitelli
mesh_terms: D003359:Cosmic Radiation; D006112:Gravitation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D010825:Physics; D013269:Stochastic Processes