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| Preface | |
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| Acknowledgments | |
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| Homogeneity and Clustering | |
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| Homogeneity and clustering | |
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| Is the universe homogeneous? | |
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| Physical principles | |
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| How did galaxies and clusters of galaxies form? | |
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| Summary | |
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| Behavior of Irregularities in the Distribution of Matter: Newtonian Approximation | |
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| Newtonian approximation | |
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| Particle dynamics in expanding coordinates | |
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| The peculiar acceleration | |
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| Two models: the Vlasov equation and the ideal fluid | |
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| Linear perturbation approximation for [delta] | |
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| Solutions for [delta](t): p = [Lambda] = 0 | |
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| Solutions for [delta](t): effect of a uniform radiation background | |
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| Solutions for [delta](t): models with [Lambda not equal] 0 | |
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| The peculiar velocity field | |
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| Joining conditions for [delta] and [upsilon] | |
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| Critical Jeans length | |
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| Primeval magnetic field as a source for [delta rho] / [rho] | |
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| Second order perturbation theory for [delta rho] / [rho] | |
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| Spherical model | |
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| Homogeneous ellipsoid model | |
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| Caustics and pancakes | |
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| Expansion, vorticity, and shear | |
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| Origin of the rotation of galaxies | |
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| Cosmic energy equation | |
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| Spherical accretion model | |
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| Hierarchical clustering model | |
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| Fourier transform of the equations of motion | |
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| Coupling of density fluctuations | |
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| n-Point Correlation Functions: Descriptive Statistics | |
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| Statistical measures of the galaxy distribution | |
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| Fair sample hypothesis | |
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| Two-point spatial correlation function [xi](r) | |
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| Two-point correlation function: another definition | |
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| Two-point correlation function: Poisson model | |
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| Three-point correlation function | |
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| Four-point correlation function | |
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| Moments of counts of objects | |
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| Constraints on [xi] and [zeta] | |
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| Probability generating function | |
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| Estimates of P[subscript N] | |
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| Cluster model | |
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| Power spectrum | |
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| Power law model for the spectrum | |
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| Bispectrum | |
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| Cross correlation function | |
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| Angular two-point correlation function | |
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| Angular power spectrum | |
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| Estimating w([theta]) | |
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| Statistical uncertainty in the estimate of w([theta]) | |
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| Relation between angular and spatial two-point correlation functions | |
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| Small separation approximation and the scaling relation | |
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| Decoupling of magnitude and position | |
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| Relation between [xi] and w: some examples | |
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| Inversion of the equation | |
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| Angular three-point correlation function | |
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| Angular four-point correlation function | |
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| Correction for curvature and expansion | |
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| Summary of numerical results | |
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| Power spectrum of the extragalactic light | |
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| Moments of the number of neighbors | |
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| Model for P[subscript N] | |
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| Clustering models | |
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| Continuous clustering hierarchy: Mandelbrot's prescription | |
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| The mass correlation functions | |
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| Clustering hierarchy: continuity speculation | |
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| Remarks on the observations | |
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| Dynamics and Statistics | |
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| Goals | |
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| Definitions of variables and distribution functions | |
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| BBGKY hierarchy equations | |
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| Fluid limit | |
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| Evolution of the integral of [xi] | |
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| Particle conservation equations | |
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| Relative peculiar velocity dispersion | |
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| Similarity solution | |
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| Cosmic energy equation | |
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| Cosmic virial theorem | |
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| Joint distribution in position and velocity | |
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| Behavior of the halo around a cluster of galaxies | |
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| Superclusters | |
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| Problems and prospects | |
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| Relativistic Theory of the Behavior of Irregularities in an Expanding World Model | |
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| Role of the relativistic theory | |
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| Time-orthogonal coordinates | |
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| The field equations for h[subscript alpha beta] | |
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| Gravitational waves | |
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| Newtonian approximation | |
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| Linear perturbation equations for the matter | |
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| Behavior of density perturbations at wavelength [characters not reproducible] ct | |
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| Spherical model | |
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| Evolution of acoustic waves | |
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| Nonlinear acoustic waves | |
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| Incompressible flow | |
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| Behavior of collisionless particles | |
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| Linear dissipation of adiabatic perturbations | |
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| Residual fluctuations in the microwave background | |
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| Isothermal perturbations | |
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| Scenarios | |
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| Nature of the universe at high redshift | |
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| Nature of protogalaxies and protoclusters | |
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| Appendix | |
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| Models and notation | |
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| List of Abbreviations | |
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| References | |
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| Index | |