Vanishing of the anchored isoperimetric profile in bond percolation at p c

Raphaël Cerf; Barbara Dembin

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arXiv · 1903.08065

Vanishing of the anchored isoperimetric profile in bond percolation at p c

Raphaël Cerf·Barbara Dembin

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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. 2019-03-19. Vanishing of the anchored isoperimetric profile in bond percolation at p c. https://arxiv.org/abs/1903.08065

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