For two-valued i.i.d. edge weights on Z^2, the event that the constrained left-right crossing time exceeds its median is noise sensitive up to width about n^{1/2}, improving the prior n^{1/22}, and conditional curvature assumptions extend this to all widths and yield a new variance lower bound.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.PR 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Noise sensitivity and variance lower bound for minimal left-right crossing of a square in first-passage percolation
For two-valued i.i.d. edge weights on Z^2, the event that the constrained left-right crossing time exceeds its median is noise sensitive up to width about n^{1/2}, improving the prior n^{1/22}, and conditional curvature assumptions extend this to all widths and yield a new variance lower bound.