Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous * - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Electronic Communications in Probability Année : 2020

Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous *

Résumé

We consider an i.i.d. supercritical bond percolation on Z^d , every edge is open with a probability p > p_c (d), where p_c (d) denotes the critical parameter for this percolation. We know that there exists almost surely a unique infinite open cluster C_p [7]. We are interested in the regularity properties in p of the anchored isoperimetric profile of the infinite cluster C_p. For d ≥ 2, we prove that the anchored isoperimetric profile defined in [4] is Lipschitz continuous on all intervals [p_0 , p_1 ] ⊂ (p_c (d), 1).
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hal-01964886 , version 1 (24-12-2018)

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Barbara Dembin. Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous *. Electronic Communications in Probability, 2020, 25, ⟨10.1214/20-ecp313⟩. ⟨hal-01964886⟩
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