Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher

Abstract : Let d ≥ 2. 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 point. We condition on the event that 0 belongs to the infinite cluster C_∞ and we consider connected subgraphs of C_∞ having at most n^d vertices and containing 0. Among these subgraphs, we are interested in the ones that minimize the open edge boundary size to volume ratio. These minimizers properly rescaled converge towards a translate of a deterministic shape and their open edge boundary size to volume ratio properly rescaled converges towards a deterministic constant.
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https://hal.archives-ouvertes.fr/hal-01905034
Contributor : Barbara Dembin <>
Submitted on : Thursday, October 25, 2018 - 3:13:32 PM
Last modification on : Wednesday, April 3, 2019 - 1:28:08 AM
Document(s) archivé(s) le : Saturday, January 26, 2019 - 2:57:09 PM

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  • HAL Id : hal-01905034, version 1
  • ARXIV : 1810.11239

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Barbara Dembin. Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher. 2018. ⟨hal-01905034⟩

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