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Record ages of non-Markovian scale-invariant random walks

Author

Listed:
  • Léo Régnier

    (CNRS/Sorbonne Université)

  • Maxim Dolgushev

    (CNRS/Sorbonne Université)

  • Olivier Bénichou

    (CNRS/Sorbonne Université)

Abstract

How long is needed for an observable to exceed its previous highest value and establish a new record? This time, known as the age of a record plays a crucial role in quantifying record statistics. Until now, general methods for determining record age statistics have been limited to observations of either independent random variables or successive positions of a Markovian (memoryless) random walk. Here we develop a theoretical framework to determine record age statistics in the presence of memory effects for continuous non-smooth processes that are asymptotically scale-invariant. Our theoretical predictions are confirmed by numerical simulations and experimental realisations of diverse representative non-Markovian random walk models and real time series with memory effects, in fields as diverse as genomics, climatology, hydrology, geology and computer science. Our results reveal the crucial role of the number of records already achieved in time series and change our view on analysing record statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-41945-9
    DOI: 10.1038/s41467-023-41945-9
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    References listed on IDEAS

    as
    1. Léo Régnier & Maxim Dolgushev & S. Redner & Olivier Bénichou, 2023. "Universal exploration dynamics of random walks," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    2. N. Levernier & T. V. Mendes & O. Bénichou & R. Voituriez & T. Guérin, 2022. "Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
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