Long Range Percolation Mixing Time

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).

Proof of Proposition 2.1 corrected

References in corpus (2)

• On the scaling of the chemical distance in long-range percolation models
• The Evolution of the Mixing Rate

Cited by in corpus (1)

• Heat kernel estimates for strongly recurrent random walk on random media