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Laplace’s first law of errors applied to diffusive motion

Author

Listed:
  • Omer Hamdi

    (Bar-Ilan University
    Bar-Ilan University)

  • Stanislav Burov

    (Bar-Ilan University)

  • Eli Barkai

    (Bar-Ilan University
    Bar-Ilan University)

Abstract

In biological, glassy, and active systems, various tracers exhibit Laplace-like, i.e., exponential, spreading of the diffusing packet of particles. The limitations of the central limit theorem in fully capturing the behaviors of such diffusive processes, especially in the tails, have been studied using the continuous time random walk model. For cases when the jump length distribution is super-exponential, e.g., a Gaussian, we use large deviations theory and relate it to the appearance of exponential tails. When the jump length distribution is sub-exponential, the packet of spreading particles is described by the big jump principle. We demonstrate the applicability of our approach for finite time, indicating that rare events and the asymptotics of the large deviations rate function can be sampled for large length scales within a reasonably short measurement time. Graphical abstract The universality of Laplace tails appears everywhere

Suggested Citation

  • Omer Hamdi & Stanislav Burov & Eli Barkai, 2024. "Laplace’s first law of errors applied to diffusive motion," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-13, June.
  • Handle: RePEc:spr:eurphb:v:97:y:2024:i:6:d:10.1140_epjb_s10051-024-00704-5
    DOI: 10.1140/epjb/s10051-024-00704-5
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    Cited by:

    1. Giorgio Kaniadakis & Tiziana Di Matteo & Antonio Maria Scarfone & Giampiero Gervino, 2024. "New trends in statistical physics of complex systems: theoretical and experimental approaches," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(12), pages 1-3, December.

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