The Annals of Probability

Uniqueness of the infinite entangled component in three-dimensional bond percolation

Olle Häggström

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Abstract

We prove uniqueness of the infinite entangled component for bond percolation on the three-dimensional cubic lattice above the entanglement critical probability. This improves earlier results by Grimmett and Holroyd.

Article information

Source
Ann. Probab., Volume 29, Number 1 (2001), 127-136.

Dates
First available in Project Euclid: 21 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aop/1008956325

Digital Object Identifier
doi:10.1214/aop/1008956325

Mathematical Reviews number (MathSciNet)
MR1825145

Zentralblatt MATH identifier
1013.60083

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Keywords
Entanglement percolation uniqueness monotonicity

Citation

Häggström, Olle. Uniqueness of the infinite entangled component in three-dimensional bond percolation. Ann. Probab. 29 (2001), no. 1, 127--136. doi:10.1214/aop/1008956325. https://projecteuclid.org/euclid.aop/1008956325


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References

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