Vanishing of the anchored isoperimetric profile in bond percolation at \(p_c\)

DOI10.1214/19-ECP281zbMath1428.60135arXiv1903.08065OpenAlexW2922511542MaRDI QIDQ2285766

Barbara Dembin, Raphaël Cerf

Publication date: 9 January 2020

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.08065

zbMATH Keywords

isoperimetric constantcritical percolation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (3)

Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous ⋮ Limit of the Wulff crystal when approaching criticality for isoperimetry in 2D percolation ⋮ Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher

Cites Work

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• Percolation in half-spaces: Equality of critical densities and continuity of the percolation probability
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• Existence and continuity of the flow constant in first passage percolation
• The supercritical phase of percolation is well behaved
• Percolation
• Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher

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