Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher

@article{Dembin2018ExistenceOT,
  title={Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher},
  author={Barbara Dembin},
  journal={arXiv: Probability},
  year={2018}
}
Let $d\geq 2$. We consider an i.i.d. supercritical bond percolation on $\mathbb{Z}^d$, every edge is open with a probability $p>p_c(d)$, where $p_c(d)$ denotes the critical point. We condition on the event that $0$ belongs to the infinite cluster $\mathcal{C}_\infty$ and we consider connected subgraphs of $\mathcal{C}_\infty$ having at most $n^d$ vertices and containing $0$. Among these subgraphs, we are interested in the ones that minimize the open edge boundary size to volume ratio. These… Expand

Figures from this paper

Vanishing of the anchored isoperimetric profile in bond percolation at $p_{c}$
Cancellation of the Anchored isoperimetric profile in bond percolation at p c.

References

SHOWING 1-10 OF 34 REFERENCES
Isoperimetry in supercritical bond percolation in dimensions three and higher
Isoperimetry in Two‐Dimensional Percolation
Limit theorems for maximum flows on a lattice
Upper large deviations for maximal flows through a tilted cylinder
Surface order large deviations for Ising, Potts and percolation models
...
1
2
3
4
...