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Statistics of the Galaxy Distribution

Statistics of the Galaxy Distribution by Vicent J. Martinez
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THE CLUMPY UNIVERSE
Galaxies
Mapping the Universe
Selection Effects and Biases
Current and Future Galaxy Catalogs
The Observed Structures: Clusters, Filaments, Walls and Voids
THE STANDARD MODEL OF THE UNIVERSE
Introduction
The Friedmann-Robertson-Walker Universe
Basic Observational Data
COSMOLOGICAL POINT PROCESSES
Introduction
Point Processes
The Relation Between Discrete and Continuous Distributions
The Two-Point Correlation Function
N-Point Correlation Functions
Moments and Counts in Cells
The Void Probability Function
Nearest Neighbor Distances
Galaxy Distribution as a Marked Point Field
FRACTAL PROPERTIES OF THE GALAXY DISTRIBUTION
Introduction
Fractal Models for the Universe
Tests on Projected Data
Fractal Dimensions
Multifractal Measures
Multiscaling
Lacunarity
STATISTICAL AND GEOMETRICAL MODELS
Introduction
The Neyman-Scott Process and Related Models
The Voronoi Model
Statistical Models for the Counts in Cells
FORMATION OF STRUCTURE
Introduction
Dynamics of Structure
The Linear Approximation
Exact Solutions
Numerical Experiments
RANDOM FIELDS IN COSMOLOGY
Introduction
Random Fields
Gaussian Random Fields
Realizations of Random Fields
Non-Gaussian Fields
Statistics of Peaks in Gaussian Random Fields
Press-Schecter Method
Halo Model of Galaxy Clustering
Stochastic and Nonlinear Biasing
FOURIER ANALYSIS OF CLUSTERING
Introduction
Estimation of Power Spectra
Redshift Distortions
Velocity Distortions in Power Spectrum
Methods for Estimating Power Spectra
Bispectrum
Low-Dimensional Samples
COSMOGRAPHY
Introduction
Potent Recipe
Wiener Filtering
Constrained Fields
Time Machines
Gravitational Lensing
STRUCTURE STATISTICS
Introduction
Topological Description
Structure Functions
Cluster and Percolation Analysis
Minimal Spanning Trees
Wavelets
Cluster Finding Algorithms
Void Statistics
Checking for Periodicity
APPENDICES
Coordinate Transformations
Some Basic Concepts in Statistics
REFERENCES
WEB SITE REFERENCES
INDEX
CRC Press; December 2001
451 pages; ISBN 9781420036169
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Title: Statistics of the Galaxy Distribution
Author: Vicent J. Martinez; Enn Saar
 
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