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2020 Vanishing of the anchored isoperimetric profile in bond percolation at $p_{c}$
Raphaël Cerf, Barbara Dembin
Electron. Commun. Probab. 25(none): 1-7 (2020). DOI: 10.1214/19-ECP281

Abstract

We consider the anchored isoperimetric profile of the infinite open cluster, defined for $p>p_{c}$, whose existence has been recently proved in [3]. We extend adequately the definition for $p=p_{c}$, in finite boxes. We prove a partial result which implies that, if the limit defining the anchored isoperimetric profile at $p_{c}$ exists, it has to vanish.

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Raphaël Cerf. Barbara Dembin. "Vanishing of the anchored isoperimetric profile in bond percolation at $p_{c}$." Electron. Commun. Probab. 25 1 - 7, 2020. https://doi.org/10.1214/19-ECP281

Information

Received: 18 March 2019; Accepted: 8 December 2019; Published: 2020
First available in Project Euclid: 4 January 2020

zbMATH: 1428.60135
Digital Object Identifier: 10.1214/19-ECP281

Subjects:
Primary: 60K35
Secondary: 82B43

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