2021
DOI: 10.48550/arxiv.2110.02603
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Biased random walk on supercritical percolation: Anomalous fluctuations in the ballistic regime

Abstract: We study biased random walk on the infinite connected component of supercritical percolation on the integer lattice Z d for d ≥ 2. For this model, Fribergh and Hammond showed the existence of an exponent γ such that: for γ < 1, the random walk is sub-ballistic (i.e. has zero velocity asymptotically), with polynomial escape rate described by γ; whereas for γ > 1, 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… Show more

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