IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1305.0639.html
   My bibliography  Save this paper

Exact record and order statistics of random walks via first-passage ideas

Author

Listed:
  • Gregory Schehr
  • Satya N. Majumdar

Abstract

While records and order statistics of independent and identically distributed (i.i.d.) random variables X_1, ..., X_N are fully understood, much less is known for strongly correlated random variables, which is often the situation encountered in statistical physics. Recently, it was shown, in a series of works, that one-dimensional random walk (RW) is an interesting laboratory where the influence of strong correlations on records and order statistics can be studied in detail. We review here recent exact results which have been obtained for these questions about RW, using techniques borrowed from the study of first-passage problems. We also present a brief review of the well known (and not so well known) results for records and order statistics of i.i.d. variables.

Suggested Citation

  • Gregory Schehr & Satya N. Majumdar, 2013. "Exact record and order statistics of random walks via first-passage ideas," Papers 1305.0639, arXiv.org.
  • Handle: RePEc:arx:papers:1305.0639
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1305.0639
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Krug, Joachim & Jain, Kavita, 2005. "Breaking records in the evolutionary race," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(1), pages 1-9.
    2. Le Doussal, Pierre & Monthus, Cécile, 2003. "Exact solutions for the statistics of extrema of some random 1D landscapes, application to the equilibrium and the dynamics of the toy model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 140-198.
    3. Gregor Wergen & Satya N. Majumdar & Gregory Schehr, 2012. "Record Statistics for Multiple Random Walks," Papers 1204.5039, arXiv.org.
    4. P. Sibani, 2007. "Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(4), pages 483-491, August.
    5. Gregor Wergen & Satya N. Majumdar & Gregory Schehr, 2012. "Record Statistics for Multiple Random Walks," Post-Print hal-00757701, HAL.
    6. Satya N. Majumdar & Philippe Mounaix & Gregory Schehr, 2013. "Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks," Post-Print hal-00861416, HAL.
    7. Satya N. Majumdar & Gregory Schehr & Gregor Wergen, 2012. "Record statistics and persistence for a random walk with a drift," Post-Print hal-00744525, HAL.
    8. Satya N. Majumdar & Gregory Schehr & Gregor Wergen, 2012. "Record statistics and persistence for a random walk with a drift," Papers 1206.6972, arXiv.org, revised Aug 2012.
    9. Gregor Wergen & Miro Bogner & Joachim Krug, 2011. "Record statistics for biased random walks, with an application to financial data," Papers 1103.0893, arXiv.org.
    10. Satya N. Majumdar & Philippe Mounaix & Gregory Schehr, 2013. "Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks," Papers 1303.4607, arXiv.org.
    11. Jean-Philippe Bouchaud & Marc Mezard, 1997. "Universality classes for extreme value statistics," Science & Finance (CFM) working paper archive 500043, Science & Finance, Capital Fund Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Srivastava, Shashi C.L. & Lakshminarayan, Arul, 2015. "Records in the classical and quantum standard map," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 67-78.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2017. "Record statistics of a strongly correlated time series: random walks and L\'evy flights," Papers 1702.00586, arXiv.org.
    2. Wergen, Gregor, 2014. "Modeling record-breaking stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 114-133.
    3. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2015. "Record statistics for random walk bridges," Papers 1505.06053, arXiv.org, revised Jan 2016.
    4. Srivastava, Shashi C.L. & Lakshminarayan, Arul, 2015. "Records in the classical and quantum standard map," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 67-78.
    5. Léo Régnier & Maxim Dolgushev & Olivier Bénichou, 2023. "Record ages of non-Markovian scale-invariant random walks," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    6. Markelov, Oleg & Nguyen Duc, Viet & Bogachev, Mikhail, 2017. "Statistical modeling of the Internet traffic dynamics: To which extent do we need long-term correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 48-60.
    7. 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.
    8. Butusov, Denis N. & Karimov, Artur I. & Pyko, Nikita S. & Pyko, Svetlana A. & Bogachev, Mikhail I., 2018. "Discrete chaotic maps obtained by symmetric integration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 955-970.
    9. Luck, J.M., 2014. "On the frequencies of patterns of rises and falls," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 252-275.
    10. 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.
    11. 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.
    12. Min, Seungsik & Shin, Ki-Hong & Baek, Woonhak & Kim, Kyungsik & You, Cheol-Hwan & Lee, Dong-In & Yum, Seong Soo & Kim, Wonheung & Chang, Ki-Ho, 2020. "Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1305.0639. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.