The Annals of Probability

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

Olle Häggström

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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.

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

First available in Project Euclid: 21 December 2001

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Zentralblatt MATH identifier

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

Entanglement percolation uniqueness monotonicity


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.

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