### 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) |
---|---|

Pages (from-to) | 559-591 |

Number of pages | 33 |

Journal | Probability Theory and Related Fields |

Volume | 106 |

Issue number | 4 |

State | Published - Dec 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Statistics and Probability

### Cite this

*Probability Theory and Related Fields*,

*106*(4), 559-591.

**Superdiffusivity in first-passage percolation.** / Licea, C.; Newman, Charles; Piza, M. S T.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 106, no. 4, pp. 559-591.

}

TY - JOUR

T1 - Superdiffusivity in first-passage percolation

AU - Licea, C.

AU - Newman, Charles

AU - Piza, M. S T

PY - 1996/12

Y1 - 1996/12

N2 - In standard first-passage percolation on ℤd (with d ≥ 2), the time-minimizing paths from a point to a plane at distance L are expected to have transverse fluctuations of order Lξ. 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.

AB - In standard first-passage percolation on ℤd (with d ≥ 2), the time-minimizing paths from a point to a plane at distance L are expected to have transverse fluctuations of order Lξ. 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.

UR - http://www.scopus.com/inward/record.url?scp=21444460424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444460424&partnerID=8YFLogxK

M3 - Article

VL - 106

SP - 559

EP - 591

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -