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.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty