Critical points of a non-Gaussian random field

2012/10/25 by T. H. Beuman, Beuman, T. H., A. M. Turner +3
Environmental Science · Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Plant Water Relations and Carbon Dynamics #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #astro-ph.CO #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.1210.6871

13 pages, 7 figures

arxiv created 2012/10/25 · openalex publication_date 2012/10/25 · arxiv updated 2012/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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