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First-passage times in complex scale-invariant media

Author

Listed:
  • S. Condamin

    (Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, case 121, 4 Place Jussieu, 75005 Paris, France)

  • O. Bénichou

    (Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, case 121, 4 Place Jussieu, 75005 Paris, France)

  • V. Tejedor

    (Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, case 121, 4 Place Jussieu, 75005 Paris, France)

  • R. Voituriez

    (Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, case 121, 4 Place Jussieu, 75005 Paris, France)

  • J. Klafter

    (School of Chemistry, Tel Aviv University)

Abstract

Mean first-passage times How long does it take a random walker to reach a given target point? This quantity, called first-passage time (FPT), is important because of its role in real situations such as transport in disordered media, neuron firing, spread of diseases and target search processes. Previous methods of determining FPT properties were effectively limited to one-dimensional geometries or to homogeneous media. Condamin et al. have developed a general theory that allows the accurate evaluation of the mean FPT in complex media. The predictions are confirmed by numerical simulations of several models of disordered media, fractals, anomalous diffusion and scale-free networks, including a yeast protein interaction network.

Suggested Citation

  • 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.
    • Handle: RePEc:nat:nature:v:450:y:2007:i:7166:d:10.1038_nature06201
    DOI: 10.1038/nature06201
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    Cited by:

    1. Le, Anbo & Gao, Fei & Xi, Lifeng & Yin, Shuhua, 2015. "Complex networks modeled on the Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 646-657.
    2. Huang, Wei & Chen, Shengyong & Wang, Wanliang, 2014. "Navigation in spatial networks: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 132-154.
    3. Henrik Seckler & Ralf Metzler, 2022. "Bayesian deep learning for error estimation in the analysis of anomalous diffusion," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    4. Zhang, Jingyuan & Xiang, Yonghong & Sun, Weigang, 2018. "A discrete random walk on the hypercube," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 1-7.
    5. Wijesundera, Isuri & Halgamuge, Malka N. & Nirmalathas, Ampalavanapillai & Nanayakkara, Thrishantha, 2016. "MFPT calculation for random walks in inhomogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 986-1002.
    6. Khajehnejad, Moein, 2019. "Efficiency of long-range navigation on Treelike fractals," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 102-110.
    7. Telcs, András & Csernai, Márton & Gulyás, András, 2013. "Load balanced diffusive capture process on homophilic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 510-519.
    8. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    9. 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.
    10. O’Keeffe, Kevin & Santi, Paolo & Wang, Brandon & Ratti, Carlo, 2021. "Urban sensing as a random search process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    11. Chełminiak, Przemysław, 2024. "First-passage time statistics for non-linear diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    12. Zhao, Dan & Ji, Shou-feng & Wang, He-ping & Jiang, Li-wen, 2021. "How do government subsidies promote new energy vehicle diffusion in the complex network context? A three-stage evolutionary game model," Energy, Elsevier, vol. 230(C).

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