PreprintarXiv licencearXiv
Fluctuation bounds for rotationally invariant first-passage percolation
Abstract
We prove that in rotationally invariant first-passage percolation on ℝd with d≥2, the passage time Tn over a distance n satisfies 𝔼[exp(|Tn−μn|/n1/2(1−ε))]≤ C for some ε>0, where μ is the time constant. This implies that its variance is at most a constant times n1−ε, the bound that Basu, Sidoravicius and Sly proved in the planar case. As in their work, our argument is an induction on the scale, but in place of their proof that the geodesic is chaotic, we use the averaging argument of Benjamini, Kalai and Schramm together with a logarithmic improvement of the Efron-Stein inequality due to Benaïm and Rossignol.
Related
- Phase Transition and Fluctuation Results for First-Passage Percolation on Spread-Out Cycle Graphs
- Variance lower bounds for geometric functionals of rotationally invariant log-concave random polytopes
- Invariance in half-space last passage percolation and directed polymers
- Stationary Half-space Geometric Last Passage Percolation without Random Shift
- Half-space last passage percolation with inhomogeneous first row
BibTeX
@misc{armstrong2026fluctuation,
title = {{Fluctuation bounds for rotationally invariant first-passage percolation}},
author = {Scott Armstrong and Ahmed Bou-Rabee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42124},
eprint = {2610.42124},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42124},
}
RIS
TY - UNPB
TI - Fluctuation bounds for rotationally invariant first-passage percolation
AU - Scott Armstrong
AU - Ahmed Bou-Rabee
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42124
UR - https://arxiv.org/abs/2610.42124
AB - We prove that in rotationally invariant first-passage percolation on ℝ^d with d≥2, the passage time T_n over a distance n satisfies 𝔼[exp(|T_n−μn|/n^1/2(1−ε))]≤ C for some ε>0, where μ is the time constant. This implies that its variance is at most a constant times n^1−ε, the bound that Basu, Sidoravicius and Sly proved in the planar case. As in their work, our argument is an induction on the scale, but in place of their proof that the geodesic is chaotic, we use the averaging argument of Benjamini, Kalai and Schramm together with a logarithmic improvement of the Efron-Stein inequality due to Benaïm and Rossignol.
ER -