The Statistics of Peaks of Gaussian Random Fields

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 |