### Abstract

In standard first-passage percolation on ℤ^{d} (with d ≥ 2), the time-minimizing paths from a point to a plane at distance L are expected to have transverse fluctuations of order L^{ξ}. It has been conjectured that ξ(d) ≥ 1/2 with the inequality strict (superdiffusivity) at least for low d and with ξ(2) = 2/3. We prove (versions of) ξ(d) ≥ 1/2 for all d and ξ(2) ≥ 3/5.

Original language | English (US) |
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Pages (from-to) | 559-591 |

Number of pages | 33 |

Journal | Probability Theory and Related Fields |

Volume | 106 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1996 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Licea, C., Newman, C. M., & Piza, M. S. T. (1996). Superdiffusivity in first-passage percolation.

*Probability Theory and Related Fields*,*106*(4), 559-591. https://doi.org/10.1007/s004400050075