Long Range Percolation Mixing Time
Itai Benjamini, Noam Berger, Ariel Yadin
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 N2 only to N(s-1) (up to poly-logarithmic factors).
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