Sublinear variance in first-passage percolation for general distributions
Probability
2016-11-21 v2
Abstract
We prove that the variance of the passage time from the origin to a point x in first-passage percolation on Z^d is sublinear in the distance to x when d \geq 2, obeying the bound Cx/(log x), under minimal assumptions on the edge-weight distribution. The proof applies equally to absolutely continuous, discrete and singular continuous distributions and mixtures thereof, and requires only 2+log moments. The main result extends work of Benjamini-Kalai-Schramm and Benaim-Rossignol.
Keywords
Cite
@article{arxiv.1306.1197,
title = {Sublinear variance in first-passage percolation for general distributions},
author = {Michael Damron and Jack Hanson and Philippe Sosoe},
journal= {arXiv preprint arXiv:1306.1197},
year = {2016}
}
Comments
32 pages. We added a proof sketch and fixed the proof of Theorem 2.3 and the bound on term (6.18)