English

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