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Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks

Author

Listed:
  • N. Levernier

    (Aix Marseille Univ., Université de Toulon, CNRS, CPT, Turing Center for Living Systems)

  • T. V. Mendes

    (Laboratoire Ondes et Matière d’Aquitaine, University of Bordeaux, Unité Mixte de Recherche 5798, CNRS)

  • O. Bénichou

    (Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC)

  • R. Voituriez

    (Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC
    Laboratoire Jean Perrin, CNRS/UPMC)

  • T. Guérin

    (Laboratoire Ondes et Matière d’Aquitaine, University of Bordeaux, Unité Mixte de Recherche 5798, CNRS)

Abstract

Persistence, defined as the probability that a signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. Often, persistence decays algebraically with time with non trivial exponents. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non-perturbative determination of persistence exponents of Gaussian non-Markovian processes with non stationary dynamics relaxing to a steady state after an initial perturbation. Two situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32280-6
    DOI: 10.1038/s41467-022-32280-6
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    References listed on IDEAS

    as
    1. S. Condamin & O. Bénichou & V. Tejedor & R. Voituriez & J. Klafter, 2007. "First-passage times in complex scale-invariant media," Nature, Nature, vol. 450(7166), pages 77-80, November.
    2. N. Levernier & M. Dolgushev & O. Bénichou & R. Voituriez & T. Guérin, 2019. "Survival probability of stochastic processes beyond persistence exponents," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
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    Cited by:

    1. 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.

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