Abstract
We study biased random walk on the infinite connected component of supercritical percolation on the integer lattice for . For this model, Fribergh and Hammond showed the existence of an exponent γ such that: for , the random walk is sub-ballistic (i.e. has zero velocity asymptotically), with polynomial escape rate described by γ; whereas for , the random walk is ballistic, with non-zero speed in the direction of the bias. They moreover established, under the usual diffusive scaling about the mean distance travelled by the random walk in the direction of the bias, a central limit theorem when . In this article, we explain how Fribergh and Hammond’s percolation estimates further allow it to be established that for the fluctuations about the mean are of an anomalous polynomial order, with exponent given by .
Funding Statement
This research was partially supported by JSPS KAKENHI, grant numbers 17H01093 and 19K03540 and by NUS grant R-146-000-260-114.
Acknowledgments
This research was initiated whilst AB was visiting DC at the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
Citation
Adam M. Bowditch. David A. Croydon. "Biased random walk on supercritical percolation: anomalous fluctuations in the ballistic regime." Electron. J. Probab. 27 1 - 22, 2022. https://doi.org/10.1214/22-EJP794
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