Long-range percolation mixing time

Authors:
Itai Benjamini;Noam Berger;Ariel Yadin
Affiliations:
Weizmann institute of science, rehovot 76100, israel (e-mail: itai.benjamini@weizmann.ac.il, ariel.yadin@weizmann.ac.il);Mathematics department, ucla, los angeles, ca 90095-1555, usa (e-mail: berger@math.ucla.edu);Weizmann institute of science, rehovot 76100, israel (e-mail: itai.benjamini@weizmann.ac.il, ariel.yadin@weizmann.ac.il)
Venue:
Combinatorics, Probability and Computing
Year:
2008

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Abstract

We provide an estimate, sharp up to poly-logarithmic factors, of the asymptotic almost sure mixing time of the graph created by long-range percolation on the cycle of length N ($\Integer/N\Integer$). While it is known that the asymptotic almost sure diameter drops from linear to poly-logarithmic as the exponent s decreases below 2 [4, 9], the asymptotic almost sure mixing time drops from N2 only to Ns-1 (up to poly-logarithmic factors).