Critical phenomena in natural sciences. Chaos, fractals, selforganization and disorder: concepts and tools
The book introduces into a large variety of topics, most of which belong to or are related to statistical physics. The first six chapters deal with basic concepts, mainly probability, fractals, and statistics, including -- on a heuristic level -- limit theorems, large deviations, and extreme value theorems. Probability distributions on the real line are discussed in some detail, emphasizing power laws and distributions with heavy tails. This introductory part of the book comprises about 160 pages. The following twelve chapters provide brief descriptions of diverse models and results, amongst them long-range correlations, phase transitions, bifurcations, the renormalization group, percolation, rupture models, self-organized criticality, and random spin systems. The amount of material covered in the book is impressive; the list of references comprises 832 entries. The author's goal is to present concepts and results in the simplest and most intuitive way rather than emphasizing mathematical rigor. The global view and the vast amount of topics covered by this book may be of value for engineers, physicists, and for other scientists, in particular from geophysics and meteorology. For mathematicians the book may be useful in order to get an idea about how mathematical results are appreciated from the applications' side, and what mathematics is expected to do for applications.
scientific article; zbMATH DE number 1541845