English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 $0$ belongsto the infinite cluster $\mathcal{C}_\infty$ and we consider connectedsubgraphs of $\mathcal{C}_\infty$ having at most $n^d$ vertices and containing$0$. Among these subgraphs, we are interested in the ones that minimize theopen edge boundary size to volume ratio. These minimizers properly rescaledconverge towards a translate of a deterministic shape and their open edgeboundary size to volume ratio properly rescaled converges towards adeterministic constant.

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