Superdiffusivity in first-passage percolation

C. Licea; C. M. Newman; M. S.T. Piza

doi:10.1007/s004400050075

Superdiffusivity in first-passage percolation

C. Licea, C. M. Newman, M. S.T. Piza

Mathematics

Research output: Contribution to journal › Article › peer-review

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
DOIs	https://doi.org/10.1007/s004400050075
State	Published - Dec 1996

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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AU - Piza, M. S.T.

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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.

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Superdiffusivity in first-passage percolation

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