| Preface | p. xi |
| Acknowledgments | p. xv |
| Homogeneity and Clustering | p. 3 |
| Homogeneity and clustering | p. 3 |
| Is the universe homogeneous? | p. 3 |
| Physical principles | p. 11 |
| How did galaxies and clusters of galaxies form? | p. 18 |
| Summary | p. 35 |
| Behavior of Irregularities in the Distribution of Matter: Newtonian Approximation | p. 37 |
| Newtonian approximation | p. 37 |
| Particle dynamics in expanding coordinates | p. 41 |
| The peculiar acceleration | p. 43 |
| Two models: the Vlasov equation and the ideal fluid | p. 45 |
| Linear perturbation approximation for [delta] | p. 49 |
| Solutions for [delta](t): p = [Lambda] = 0 | p. 51 |
| Solutions for [delta](t): effect of a uniform radiation background | p. 56 |
| Solutions for [delta](t): models with [Lambda not equal] 0 | p. 59 |
| The peculiar velocity field | p. 63 |
| Joining conditions for [delta] and [upsilon] | p. 66 |
| Critical Jeans length | p. 68 |
| Primeval magnetic field as a source for [delta rho] / [rho] | p. 71 |
| Second order perturbation theory for [delta rho] / [rho] | p. 74 |
| Spherical model | p. 77 |
| Homogeneous ellipsoid model | p. 86 |
| Caustics and pancakes | p. 95 |
| Expansion, vorticity, and shear | p. 103 |
| Origin of the rotation of galaxies | p. 107 |
| Cosmic energy equation | p. 110 |
| Spherical accretion model | p. 115 |
| Hierarchical clustering model | p. 120 |
| Fourier transform of the equations of motion | p. 124 |
| Coupling of density fluctuations | p. 128 |
| n-Point Correlation Functions: Descriptive Statistics | p. 138 |
| Statistical measures of the galaxy distribution | p. 138 |
| Fair sample hypothesis | p. 142 |
| Two-point spatial correlation function [xi](r) | p. 143 |
| Two-point correlation function: another definition | p. 145 |
| Two-point correlation function: Poisson model | p. 147 |
| Three-point correlation function | p. 148 |
| Four-point correlation function | p. 150 |
| Moments of counts of objects | p. 152 |
| Constraints on [xi] and [zeta] | p. 156 |
| Probability generating function | p. 158 |
| Estimates of P[subscript N] | p. 160 |
| Cluster model | p. 163 |
| Power spectrum | p. 166 |
| Power law model for the spectrum | p. 169 |
| Bispectrum | p. 171 |
| Cross correlation function | p. 172 |
| Angular two-point correlation function | p. 174 |
| Angular power spectrum | p. 175 |
| Estimating w([theta]) | p. 183 |
| Statistical uncertainty in the estimate of w([theta]) | p. 187 |
| Relation between angular and spatial two-point correlation functions | p. 189 |
| Small separation approximation and the scaling relation | p. 191 |
| Decoupling of magnitude and position | p. 194 |
| Relation between [xi] and w: some examples | p. 195 |
| Inversion of the equation | p. 200 |
| Angular three-point correlation function | p. 203 |
| Angular four-point correlation function | p. 209 |
| Correction for curvature and expansion | p. 213 |
| Summary of numerical results | p. 221 |
| Power spectrum of the extragalactic light | p. 225 |
| Moments of the number of neighbors | p. 230 |
| Model for P[subscript N] | p. 233 |
| Clustering models | p. 236 |
| Continuous clustering hierarchy: Mandelbrot's prescription | p. 243 |
| The mass correlation functions | p. 249 |
| Clustering hierarchy: continuity speculation | p. 253 |
| Remarks on the observations | p. 255 |
| Dynamics and Statistics | p. 257 |
| Goals | p. 257 |
| Definitions of variables and distribution functions | p. 258 |
| BBGKY hierarchy equations | p. 259 |
| Fluid limit | p. 262 |
| Evolution of the integral of [xi] | p. 264 |
| Particle conservation equations | p. 266 |
| Relative peculiar velocity dispersion | p. 272 |
| Similarity solution | p. 275 |
| Cosmic energy equation | p. 278 |
| Cosmic virial theorem | p. 280 |
| Joint distribution in position and velocity | p. 284 |
| Behavior of the halo around a cluster of galaxies | p. 291 |
| Superclusters | p. 299 |
| Problems and prospects | p. 301 |
| Relativistic Theory of the Behavior of Irregularities in an Expanding World Model | p. 304 |
| Role of the relativistic theory | p. 304 |
| Time-orthogonal coordinates | p. 306 |
| The field equations for h[subscript alpha beta] | p. 310 |
| Gravitational waves | p. 312 |
| Newtonian approximation | p. 313 |
| Linear perturbation equations for the matter | p. 317 |
| Behavior of density perturbations at wavelength [characters not reproducible] ct | p. 319 |
| Spherical model | p. 324 |
| Evolution of acoustic waves | p. 330 |
| Nonlinear acoustic waves | p. 333 |
| Incompressible flow | p. 341 |
| Behavior of collisionless particles | p. 345 |
| Linear dissipation of adiabatic perturbations | p. 352 |
| Residual fluctuations in the microwave background | p. 363 |
| Isothermal perturbations | p. 373 |
| Scenarios | p. 379 |
| Nature of the universe at high redshift | p. 379 |
| Nature of protogalaxies and protoclusters | p. 384 |
| Appendix | p. 395 |
| Models and notation | p. 395 |
| List of Abbreviations | p. 401 |
| References | p. 402 |
| Index | p. 417 |
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