Critical Phenomena in Natural Sciences

1. Front Matter

   Pages I-XXII

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2. Useful Notions of Probability Theory

   Pages 1-31

3. Sums of Random Variables, Random Walks and the Central Limit Theorem

   Pages 33-57

4. Large Deviations

   Pages 59-91

5. Power Law Distributions

   Pages 93-121

6. Fractals and Multifractals

   Pages 123-161

7. Rank-Ordering Statistics and Heavy Tails

   Pages 163-197

8. Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”

   Pages 199-221

9. Long-Range Correlations

   Pages 223-240

10. Phase Transitions: Critical Phenomena and First-Order Transitions

    Pages 241-254

11. Transitions, Bifurcations and Precursors

    Pages 255-266

12. The Renormalization Group

    Pages 267-292

13. The Percolation Model

    Pages 293-311

14. Rupture Models

    Pages 313-344

15. Mechanisms for Power Laws

    Pages 345-394

16. Self-Organized Criticality

    Pages 395-439

17. Introduction to the Physics of Random Systems

    Pages 441-456

18. Randomness and Long-Range Laplacian Interactions

    Pages 457-475

19. Back Matter

    Pages 477-529

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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. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.

• Renormalization group
• critical phenomena
• long-range interactions
• mechanics
• power laws
• random walks
• self-organized criticality
• statistical physics

• Department of Management, Technology and Economics (D-MTEC), ETH Zentrum, Zürich, Switzerland

  Didier Sornette

• Laboratoire de Physique de la Matière Condensée, CNRS UMR6622, Université de Nice-Sophia Antipolis, Faculté des Sciences, Nice Cedex 2, France

  Didier Sornette

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