Titlebook: Critical Phenomena in Natural Sciences; Chaos, Fractals, Sel Didier Sornette Textbook 20001st edition Springer-Verlag Berlin Heidelberg 200

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0172-7389 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.978-3-662-04174-1Series ISSN 0172-7389 Series E-ISSN 2198-333X

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Sums of Random Variables, Random Walks and the Central Limit Theorem,aussian law (see below). In fact, it is hard to find an observation that is . controlled by many variables. Studying the sum of random variables allows us to grasp the fundamental notion of collective behavior without the need for further complications.

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Rank-Ordering Statistics and Heavy Tails,he largest floods and largest storms provide major erosion boosts and so on. It is thus of utmost interest and importance to characterize these large events and their distributions. However, by definition, the statistics of rare events is limited and the distributions are thus difficult to constrain.

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,Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”,on of entropy . is small for a given variation of . of energy, the temperature is large: the system is sufficiently excited and disordered that the entropy (which roughly quantifies the number of excited states) is almost insensitive to the energy.

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Sums of Random Variables, Random Walks and the Central Limit Theorem,any contributions or are the result of many effects. The pressure in a room, measured on a surface, is the sum of the order of 10. momentum exchanges between the air molecules and the surface. The large time tectonic deformation is the (tensorial) sum of the deformation associated with the myriad of