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Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications.
Probability.- Sums of Random Variables, Random Walks and the Central Limit Theorem.- The Stable Laws: Gaussian and Levy Laws.- Power Laws.- Statistical Approach to Hypothesis Testing.- Probabilistic Derivation of Statistical Mechanics: General Introduction of the Concept of "Temperature". The Multifractional Formalism and Improved Method to Correct for Finite Size Effects and Irregular Geometries.- The Rank-Ordering Method for the Determination of Distribution Tails.- Long-Range Correlations.- Critical Phenomena.- Transitions, Bifurcations and Precursors.- The Renormalization Group.- The Percolation Model.- The Branching Model.- Simple Rupture Models.- Directed Percolation.- From Chaos to Spatio-Temporal Chaos to Turbulence.- Scale Invariance and Fractals.- Simple Mechanisms to Generate Power Laws.- SOC.- Levy-Distributions from Random Distributions of Sources with Long-Range Interactions.- Long-Range Forces due to Irregular Arrays of Sources at Boundaries.- Anomalous Relaxation. And much more....