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Non Gaussian extrema counts for CMB maps

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arxiv 1107.1863 v1 pith:QW5KGCDA submitted 2011-07-10 astro-ph.CO math-phmath.MP

classification astro-ph.COmath-phmath.MP
keywords countsgaussianextremamapsorderanalysisanalyticarbitrary
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In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian "Planck" data.

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Cited by 2 Pith papers

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  1. Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams

    astro-ph.CO 2019-08 conditional novelty 5.0 of 10

    The paper introduces a Morse-graph formalism that yields approximate, one-parameter-fitted formulas for expected Betti numbers of 2D Gaussian random fields and shows these homology statistics are sensitive to local no...

  2. Understanding the non-Gaussian nature of Galactic foreground emissions towards small scales

    astro-ph.CO 2026-06 unverdicted novelty 4.0 of 10

    Galactic foregrounds display a universal excess-kurtosis non-Gaussian signature stable across scales that arises from heavy-tailed one-point statistics plus steep spatial correlations.

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