Summary.
In standard first-passage percolation on \({\Bbb Z}^d\) (with \(d\geq 2\)), the time-minimizing paths from a point to a plane at distance \(L\) are expected to have transverse fluctuations of order \(L^\xi\). It has been conjectured that \(\xi(d)\geq 1/2\) with the inequality strict (superdiffusivity) at least for low \(d\) and with \(\xi(2)=2/3\). We prove (versions of) \(\xi(d)\geq 1/2\) for all \(d\) and \(\xi(2)\geq 3/5\).
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Received: 30 August 1995 / In revised form: 28 March 1996
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Licea, C., Newman, C. & Piza, M. Superdiffusivity in first-passage percolation. Probab Theory Relat Fields 106, 559–591 (1996). https://doi.org/10.1007/s004400050075
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DOI: https://doi.org/10.1007/s004400050075