Preprints, Working Papers, ... Year : 2019

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

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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Dates and versions

hal-02071030 , version 1 (18-03-2019)
hal-02071030 , version 2 (17-12-2019)

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Raphaël Cerf, Barbara Dembin. Vanishing of the anchored isoperimetric profile in bond percolation at p c. 2019. ⟨hal-02071030v2⟩
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