Abstract
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.
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