Critical points of a non-Gaussian random field

TL;DR

This paper introduces a mathematical framework to detect and quantify non-Gaussian features in random fields by analyzing the imbalance between maxima and minima in scalar fields, applicable to various natural phenomena.

Contribution

It presents a new, simple method based on counting maxima and minima to investigate non-Gaussian contributions in scalar random fields, extending analysis beyond Gaussian assumptions.

Findings

Non-Gaussianity causes imbalance between maxima and minima densities.

The method quantifies non-Gaussian contributions in smooth 2D surfaces.

Applicable to diverse fields with scalar surface data.

Abstract

Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and minima of a scalar field. We consider a random surface, whose height is given by a nonlinear function of a Gaussian field. We find that, as a result of the non-Gaussianity, the density of maxima and minima no longer match and calculate the relative imbalance between the two. Our approach allows to detect and quantify non-Gaussianities present in any random field that can be represented as the height of a smooth two-dimensional surface.