Ebook: Statistical Physics for Cosmic Structures
- Tags: Statistical Physics, Mathematical Methods in Physics, Astronomy Astrophysics and Cosmology, Relativity and Cosmology
- Year: 2005
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages I-XV
Introduction....Pages 1-23
Front Matter....Pages 25-25
Uniform and Correlated Mass Density Fields....Pages 27-72
The Power Spectrum and the Classification of Stationary Stochastic Fields....Pages 73-99
Fractals....Pages 101-142
Multifractals and Mass Distributions....Pages 143-163
Front Matter....Pages 165-165
Fluctuations in Standard Cosmological Models: A Real Space View....Pages 167-191
Discrete Representation of Fluctuations in Cosmological Models....Pages 193-217
Galaxy Surveys: An Introduction to Their Analysis....Pages 219-233
Characterizing the Observed Distribution of Visible Matter I: The Conditional Average Density in Galaxy Catalogs....Pages 235-263
Characterizing the Observed Distribution of Visible Matter II: Number Counts and Their Fluctuations....Pages 265-289
Luminosity in Galaxy Correlations....Pages 291-297
The Distribution of Galaxy Clusters....Pages 299-311
Biasing a Gaussian Random Field and the Problem of Galaxy Correlations....Pages 313-333
The Gravitational Field in Stochastic Particle Distributions....Pages 335-361
Back Matter....Pages 363-424
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.
Content:
Front Matter....Pages I-XV
Introduction....Pages 1-23
Front Matter....Pages 25-25
Uniform and Correlated Mass Density Fields....Pages 27-72
The Power Spectrum and the Classification of Stationary Stochastic Fields....Pages 73-99
Fractals....Pages 101-142
Multifractals and Mass Distributions....Pages 143-163
Front Matter....Pages 165-165
Fluctuations in Standard Cosmological Models: A Real Space View....Pages 167-191
Discrete Representation of Fluctuations in Cosmological Models....Pages 193-217
Galaxy Surveys: An Introduction to Their Analysis....Pages 219-233
Characterizing the Observed Distribution of Visible Matter I: The Conditional Average Density in Galaxy Catalogs....Pages 235-263
Characterizing the Observed Distribution of Visible Matter II: Number Counts and Their Fluctuations....Pages 265-289
Luminosity in Galaxy Correlations....Pages 291-297
The Distribution of Galaxy Clusters....Pages 299-311
Biasing a Gaussian Random Field and the Problem of Galaxy Correlations....Pages 313-333
The Gravitational Field in Stochastic Particle Distributions....Pages 335-361
Back Matter....Pages 363-424
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