IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v494y2018icp1-7.html
   My bibliography  Save this article

A discrete random walk on the hypercube

Author

Listed:
  • Zhang, Jingyuan
  • Xiang, Yonghong
  • Sun, Weigang

Abstract

In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determine the exponent of scaling efficiency characterizing the random walks and compare it with those of the existing networks. Finally we study the random walks on the hypercube with a located trap and provide a solution of the Kirchhoff index of the hypercube.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:494:y:2018:i:c:p:1-7
    DOI: 10.1016/j.physa.2017.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117312487
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.12.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shunqi Wu & Zhongzhi Zhang & Guanrong Chen, 2011. "Random walks on dual Sierpinski gaskets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 82(1), pages 91-96, July.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    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. Khajehnejad, Moein, 2019. "Efficiency of long-range navigation on Treelike fractals," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 102-110.
    2. Chen, Yung-Pin & Goldstein, Isaac H. & Lathrop, Eve D. & Nelsen, Roger B., 2017. "Computing an expected hitting time for the 3-urn Ehrenfest model via electric networks," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 42-48.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    8. 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).
    9. 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.
    10. 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.
    11. 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.

    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:eee:phsmap:v:494:y:2018:i:c:p:1-7. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.