Long-range percolation mixing time

Itai Benjamini; Noam Berger; Ariel Yadin

doi:10.1017/S0963548308008948

Long-range percolation mixing time

Itai Benjamini, Noam Berger, Ariel Yadin

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 (ℤ/Nℤ). 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 N^s-1 (up to poly-logarithmic factors).

Original language	English
Pages (from-to)	487-494
Number of pages	8
Journal	Combinatorics Probability and Computing
Volume	17
Issue number	4
DOIs	https://doi.org/10.1017/S0963548308008948
State	Published - 1 Jul 2008
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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10.1017/S0963548308008948

Cite this

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AU - Yadin, Ariel

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AB - 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 (ℤ/Nℤ). 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).

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DO - 10.1017/S0963548308008948

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JO - Combinatorics Probability and Computing

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Long-range percolation mixing time

Abstract

ASJC Scopus subject areas

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