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

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https://doi.org/10.1007/978-3-663-02790-4We now present another aspect of quenched randomness that occurs in relation to long-range interactions.

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Power Law Distributions,Summing . i.i.d. random variables with pdf ..(.), one obtains a random variable which has in general a different pdf ..(.) given by . convolutions of P.(.) with itself as given by (2.62).

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Fractals and Multifractals,During the third century BC, Euclid and his students introduced the concept of space dimension which can take positive integer values equal to the number of independent directions. A smooth line has dimension 1, a smooth surface has dimension 2 and our space (seen at large scales) has dimension 3.

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Randomness and Long-Range Laplacian Interactions,We now present another aspect of quenched randomness that occurs in relation to long-range interactions.

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0172-7389 he 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

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Trockene und wasserhaltige Gasgemischecting elements. Studying the correlations and their consequences is an essential part of the analysis of a system since the correlations are the signatures that inform us about the underlying mechanisms.