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

Authors
  • Cerf, Raphaël
  • Dembin, Barbara
Publication Date
Mar 18, 2019
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
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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 pc exists, it has to vanish.

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