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

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01964886
Contributor : Barbara Dembin <>
Submitted on : Monday, December 24, 2018 - 9:42:35 AM
Last modification on : Friday, April 10, 2020 - 5:27:06 PM
Document(s) archivé(s) le : Monday, March 25, 2019 - 12:11:14 PM

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  • HAL Id : hal-01964886, version 1
  • ARXIV : 1901.00367

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Barbara Dembin. Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous *. 2018. ⟨hal-01964886⟩

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