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.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01905034
Contributeur : Barbara Dembin <>
Soumis le : jeudi 25 octobre 2018 - 15:13:32
Dernière modification le : vendredi 4 janvier 2019 - 17:33:38
Document(s) archivé(s) le : samedi 26 janvier 2019 - 14:57:09

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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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