Long Range Percolation Mixing Time

Details Long Range Percolation Mixing Time Long Range Percolation Mixing Time

2007-03-29

arxiv.org/abs/math/0703872v2

Combinatorics, Probability and Computing 17 (2008), 487-494

Mathematics

Probability

Proof of Proposition 2.1 corrected

Scientific paper

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).

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