Cancellation 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 pc exists, it has to vanish.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [10 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02071030
Contributor : Barbara Dembin <>
Submitted on : Monday, March 18, 2019 - 1:08:20 PM
Last modification on : Sunday, June 16, 2019 - 11:59:17 AM
Long-term archiving on : Wednesday, June 19, 2019 - 5:42:47 PM

Files

Cancellation of the Cheeger co...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02071030, version 1
  • ARXIV : 1903.08065

Citation

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

Share

Metrics

Record views

29

Files downloads

54