Long Range Percolation Mixing Time
Probability
2009-04-19 v2 Mathematical Physics
Combinatorics
math.MP
Abstract
We provide an estimate, sharp up to poly-logarithmic factors, of the asymptotically almost sure mixing time of the graph created by long-range percolation on the cycle of length N (Z/NZ). While it is known that the almost sure diameter drops from linear to poly-logarithmic as the exponent s decreases below 2, the almost sure mixing time drops from N^2 only to N^(s-1) (up to poly-logarithmic factors).
Keywords
Cite
@article{arxiv.math/0703872,
title = {Long Range Percolation Mixing Time},
author = {Itai Benjamini and Noam Berger and Ariel Yadin},
journal= {arXiv preprint arXiv:math/0703872},
year = {2009}
}
Comments
Proof of Proposition 2.1 corrected