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Long Range Percolation Mixing Time
[article]

Itai Benjamini, Noam Berger, Ariel Yadin

2009
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arXiv
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pre-print

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* ...
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). ...
Remarks • *In* the following sections we will provide upper and lower bounds on the mixing time of G s,β (N ), that match up to *poly*-*logarithmic* factors. ...

arXiv:math/0703872v2
fatcat:rma6gvde2zfzvdiiuugg7gm3gy