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

Zhongyang Zhang and Lixin Zhang

Statistics & Probability Letters, 2013, vol. 83, issue 11, 2459-2466

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.

Keywords: Long-range percolation; Random walk; Quenched invariance principle; Corrector (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2013.06.036

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