Stochastic geometry and topology of non-Gaussian fields
| Autor: | Vincenzo Vitelli, Thomas H. Beuman, Ari Turner |
|---|---|
| Přispěvatelé: | Quantum Condensed Matter Theory (ITFA, IoP, FNWI) |
| Rok vydání: | 2012 |
| Předmět: |
Cosmology and Nongalactic Astrophysics (astro-ph.CO)
Gaussian Normal Distribution FOS: Physical sciences Topology Gaussian random field symbols.namesake Non-Gaussianity Condensed Matter - Statistical Mechanics Physics Stochastic Processes Multidisciplinary Random field Statistical Mechanics (cond-mat.stat-mech) Stochastic process Models Theoretical Maxima and minima Nonlinear system Classical mechanics Nonlinear Dynamics Physical Sciences symbols Stochastic geometry Cosmic Radiation Astrophysics - Cosmology and Nongalactic Astrophysics Gravitation |
| Zdroj: | Proceedings of the National Academy of Sciences of the United States of America, 109(49), 19943-19948. National Academy of Sciences |
| ISSN: | 1091-6490 0027-8424 |
| DOI: | 10.1073/pnas.1212028109 |
| Popis: | 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. Comment: 8 pages, 4 figures |
| Databáze: | OpenAIRE |
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