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Pré-Publication, Document De Travail Année : 2019

Cancellation of the Anchored isoperimetric profile in bond percolation at p c

Raphaël Cerf
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Résumé

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 pc exists, it has to vanish.
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Dates et versions

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

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Raphaël Cerf, Barbara Dembin. Cancellation of the Anchored isoperimetric profile in bond percolation at p c. 2019. ⟨hal-02071030v1⟩
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