The physics of scale-invariant and complex systems is a novel interdisciplinary field. Its ideas allow us to look at natural phenomena in a radically new and original way, eventually leading to unifying concepts independent of the detailed structure of the systems. The objective is the study of complex, scale-invariant, and more general stochastic structures that appear both in space and time in a vast variety of natural phenomena, which exhibit new types of collective behaviors, and the fostering of their understanding. This book has been conceived as a methodological monograph in which the main methods of modern statistical physics for cosmological structures and density fields (galaxies, Cosmic Microwave Background Radiation, etc.) are presented in detail. The main purpose is to present clearly, to a workable level, these methods, with a certain mathematical accuracy, providing also some paradigmatic examples of applications. This should result in a new and more general frameworkfor the statistical analysis of the many new data concerning the different cosmic structures which characterize the large scale Universe and for their theoretical interpretation and modeling.

"The physics of scale-invariant and complex systems is a novel interdisciplinary field. Its ideas allow us to look at natural phenomena in a radically new and original way, eventually leading to unifying concepts independent of the detailed structure of the systems. The objective is the study of complex, scale-invariant, and more general stochastic structures that appear both in space and time in a vast variety of natural phenomena, which exhibit new types of collective behaviors, and the fostering of their understanding. This book has been conceived as a methodological monograph in which the main methods of modern statistical physics for cosmological structures and density fields (galaxies, Cosmic Microwave Background Radiation, etc.) are presented in detail. The main purpose is to present clearly, to a workable level, these methods, with a certain mathematical accuracy, providing also some paradigmatic examples of applications. This should result in a new and more general framework for the statistical analysis of the many new data concerning the different cosmic structures which characterize the large scale Universe and for their theoretical interpretation and modeling. TOC:Introduction.- Statistical Methods.- Statistically Homogeneous and Isotropic Distributions.- Fractals.- Multifractals and Mass Distribution.- Fractal Algorithms.- Bibliography."

Statistical Methods.- Uniform and Correlated Mass Density Fields.- The Power Spectrum and the Classification of Stationary Stochastic Fields.- Fractals.- Multifractals and Mass Distributions.- Applications to Cosmology.- Fluctuations in Standard Cosmological Models: A Real Space View.- Discrete Representation of Fluctuations in Cosmological Models.- Galaxy Surveys: An Introduction to Their Analysis.- Characterizing the Observed Distribution of Visible Matter I: The Conditional Average Density in Galaxy Catalogs.- Characterizing the Observed Distribution of Visible Matter II: Number Counts and Their Fluctuations.- Luminosity in Galaxy Correlations.- The Distribution of Galaxy Clusters.- Biasing a Gaussian Random Field and the Problem of Galaxy Correlations.- The Gravitational Field in Stochastic Particle Distributions.