Fluctuations in first-passage percolation
Probability
2018-04-17 v1
Abstract
We present a survey of techniques to obtain upper bounds for the variance of the passage time in first-passage percolation. The methods discussed are a combination of tools from the theory of concentration of measure, some of which we briefly review. These are combined with variations on an idea of Benjamini-Kalai-Schramm to obtain a logarithmic improvement over the linear bound implied by the Efron-Stein/Poincare inequality, for general edge-weight distributions.
Keywords
Cite
@article{arxiv.1804.05718,
title = {Fluctuations in first-passage percolation},
author = {Philippe Sosoe},
journal= {arXiv preprint arXiv:1804.05718},
year = {2018}
}
Comments
This is a chapter in a forthcoming AMS Proceedings collection of expanded notes from the AMS Short Course "Random Growth Models," which took place in Atlanta, GA, at the AMS Joint Mathematics Meetings in January 2017. Editors: Michael Damron, Firas Rassoul-Agha, Timo Seppalainen