Large Deviations

  • Didier Sornette
Part of the Springer Series in Synergetics book series (SSSYN)


The central limit theorem states that the Gaussian law is a good description of the center of the pdf of a sum of a large number N of random variables with finite variance and that the weight (in probability) of the tail goes to zero for large N We now make more precise what is meant by the “center” of the pdf. This section is slightly more technical that the previous ones, eventhough we emphasize a non-rigorous intuitive presentation. The purpose of this chapter is to show that there is a lot of “action” going on in the tails, beyond the central Gaussian region. This must be kept in mind for practical applications and data analysis.


Central Limit Theorem Seismic Moment Extreme Deviation Velocity Increment Lagrange Parameter 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Didier Sornette
    • 1
    • 2
  1. 1.Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, 3845 Slichter HallUniversity of CaliforniaLos AngelesUSA
  2. 2.Laboratoire de Physique de la Matière Condensée, CNRS UMR6622, Faculté des SciencesUniversité des SciencesNice Cedex 2France

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