First Passage Percolation Has Sublinear Distance Variance
By Itai Benjamini, G. Kalai, Oded Schramm. 2002
167 citations recorded by the source corpus.
Let 0 1, the distance dist ω (0, ν) from the origin to a vertex ν, | ν | > 2, has variance bounded by C |ν|/ log |ν|, where C = C (a, b, d) is a constant which may only depend on a, b and d. Some related variants are also discussed.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7b4d1c3216c08764c772169537b6f12519456064
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Mathematical Physics
- Michael Damron
- Jack Hanson
- Antonio Auffinger
- Philippe Sosoe
- Itai Benjamini
- P. Maillard
- Panagiotis E. Souganidis
- Pierre Cardaliaguet
In Statistics and Probability
- Michael Damron
- Jack Hanson
- Antonio Auffinger
- Philippe Sosoe
- Itai Benjamini
- P. Maillard
- Pierre Cardaliaguet
- S. Armstrong
Citations in the corpus
- Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations (2012, background): “In analogy with the best known variance bound in first-passage percolation, due to Benjamini, Kalai and Schramm [7], we expect that an estimate of the form”
- Geodesics in first passage percolation (2005, unknown): “Benjamini, Kalai, and Schramm proved for a class of measures that the variance of an is O(n/ log n) [2].”
- 50 years of first passage percolation (2015, methodology): “The following similar open question (a version of the “BKS midpoint problem” posed in [23]) is related to the existence of geodesic lines, which is the topic of Subsection 4.”
- Point-to-Point Distance in First Passage Percolation on (Tree) ×Z (2013, background): “whether the fluctuations are actually small (recall that in FPP on Z2, the fluctuations are believed to be of order n1/3 see e.g. [6] and up to now have only been proven to be of order at most p n/logn [1]). We therefore conclude with the following question: Question. In Td ×Zor Td−1,d ×Z, how big are”
- Sublinear variance in first-passage percolation for general distributions (2013, background): “3 Variance bound for τ (0, x) The mechanism for sublinear behavior of the variance which was identified in [4] can be understood as follows.”