Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools

By Didier Sornette. 2000

1,474 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6c6b227435ec35b6432fa91da46982a201df3ef1

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Citations in the corpus

Dragon-Kings, Black Swans and the Prediction of Crises (2009, background): “Mathematically, large stock market crashes are the social analogues of so-called critical points studied in the statistical physics community in relation to magnetism, melting, and other phase transformation of solids, liquids, gas and other phases of matter [2].”
Critical Market Crashes (2003, neutral): “The results obtained in Johansen and Sornette (1998, 2000a, 2001c, 2002) can be summarized as follows: 1.”
Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution (2000, methodology): “The normalized difference equals (<ξ>SZ - <ξ>MORZ)/((σSZ)2 + (σMORZ)2)1/2 = 7.26 8 8 which corresponds to the Gaussian probability of excess ε ≅ 2×10-13 (note that fluctuations of 1/ξ are asymptotically Gaussian (Sornette et al., 1996; Sornette, 2000)).”
On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns (2006, background): “This almost-but-not-quite Lévy stable description explains (in part) the slow convergence of the returns distribution to the Gaussian law under time aggregation (Sornette 2000).”
Stochastic Process Methods with an Application to Budgetary Data (2011, background): “Important examples for economics include stock markets (Sornette 2003) and growth processes, such as firms, universities, cities, and countries (Gabaix 1999; Podobnik et al. 2009); political science examples include forms of cooperation and conflict (Richardson 1948; Cederman 2003; Biggs 2005).”
The principles of collective animal behaviour (2006, background): “…and Prigogine the unifying theory was the thermodynamics of open systems; for Bak (1996) it was self-organized criticality and sand piles; for Sornette (2004) it is the generalization of the normal distribution to power law distributions; for Kauffman (1993) it is Boolean networks; and for…”
The distribution of wealth and …scal policy in economies with …nitely lived agents (2008, neutral): “stochastic di¤erence equations produce stationary distributions which are Pareto; see e.g., Sornette (2000) for a survey.”
The Matthew effect in empirical data (2014, background): “While many different physical mechanisms may be at the origin of power laws in complex systems, yielding possibly widely different exponents μ [6, 7, 86], preferential attachment is certainly one viable candidate.”
Effect of microstructural length scales on spall behavior of copper (2004, background): “Empirically, from scaling laws related to critical phenomena, [ 19 ] the shapes of the curves follow the approximate functional form”
Power-law distributions in binned empirical data (2012, background): “ whose populations are roughly 1000 times larger than the average. Extensive discussions of this and other properties of power laws can be found in reviews by Mitzenmacher [21], Newman [23], Sornette [33] and Gabaix [13]. Mathematically, a quantity x obeys a power law if it is drawn from a probabili”