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.
Citation
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
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