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The statistics of peaks of Gaussian random fields
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1986
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Gaussian random fields are employed to model small‑amplitude initial density fluctuations in cosmology, providing a framework for studying structure formation. The authors derive the point‑process equation for peak density, impose proper conditional probability constraints, and develop tools to compute peak‑peak correlation functions and profile shapes in Gaussian random fields. They obtain analytic expressions for the average density of maxima and upcrossing points, and demonstrate that high peaks are spatially segregated from the underlying mass distribution. Published in The Astrophysical Journal, May 1986, DOI 10.1086/164143.
view Abstract Citations (3327) References (46) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Statistics of Peaks of Gaussian Random Fields Bardeen, J. M. ; Bond, J. R. ; Kaiser, N. ; Szalay, A. S. Abstract A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima. Publication: The Astrophysical Journal Pub Date: May 1986 DOI: 10.1086/164143 Bibcode: 1986ApJ...304...15B Keywords: Cosmology; Density Distribution; Galactic Clusters; Galactic Evolution; Random Processes; Statistical Analysis; Density (Number/Volume); Mass Distribution; Mass To Light Ratios; Maxima; Missing Mass (Astrophysics); Probability Distribution Functions; Red Shift; Statistical Correlation; Velocity Distribution; Astrophysics; EARLY UNIVERSE; GALAXIES: CLUSTERING; GALAXIES: FORMATION full text sources ADS |