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Universality classes for extreme value statistics

Author

Listed:
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Marc Mezard

    (Universite Paris Sud (Orsay))

Abstract

The low temperature physics of disordered systems is governed by the statistics of extremely low energy states. It is thus rather important to discuss the possible universality classes for extreme value statistics. We compare the usual probabilistic classification to the results of the replica approach. We show in detail that one class of independent variables corresponds exactly to the so-called one step replica symmetry breaking solution in the replica language. This universality class holds if the correlations are sufficiently weak. We discuss the relation between the statistics of extremes and the problem of Burgers turbulence in decay.

Suggested Citation

  • Jean-Philippe Bouchaud & Marc Mezard, 1997. "Universality classes for extreme value statistics," Science & Finance (CFM) working paper archive 500043, Science & Finance, Capital Fund Management.
    • Handle: RePEc:sfi:sfiwpa:500043
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    Cited by:

    1. Paolo Sibani & Stefan Boettcher & Henrik Jeldtoft Jensen, 2021. "Record dynamics of evolving metastable systems: theory and applications," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-23, January.
    2. Jean Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Post-Print hal-04145594, HAL.
    3. Gregory Schehr & Satya N. Majumdar, 2013. "Exact record and order statistics of random walks via first-passage ideas," Papers 1305.0639, arXiv.org.
    4. Jean-Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Papers 2306.16165, arXiv.org.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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