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Scaling limits for one-dimensional long-range percolation: Using the corrector method

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  • Zhang, Zhongyang
  • Zhang, Lixin

Abstract

In this paper, by using the corrector method we give another proof of the quenched invariance principle for the random walk on the infinite random graph generated by a one-dimensional long-range percolation under the conditions that the connection probability p(1)=1 and the percolation exponent s>2. The key step of the proof is the construction of the corrector. We show that the corrector can be constructed under either s∈(2,3] or s>3, though the corresponding underlying measures may be different. As an application of the main result we get a new lower bound of the quenched diagonal transition probability for the random walk.

Suggested Citation

  • Zhang, Zhongyang & Zhang, Lixin, 2013. "Scaling limits for one-dimensional long-range percolation: Using the corrector method," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2459-2466.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2459-2466
    DOI: 10.1016/j.spl.2013.06.036
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    Cited by:

    1. de Almeida, M.L. & Albuquerque, E.L. & Fulco, U.L. & Serva, M., 2014. "A percolation system with extremely long range connections and node dilution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 273-278.

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