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 $\mathcal{C}^n$ be the largest open cluster for supercritical Bernoullibond percolation in $[-n, n]^d \cap \mathbb{Z}^d$ with $d \ge 2$. We obtain asharp estimate for the effective resistance on $\mathcal{C}^n$. As anapplication we show that the cover time for the simple random walk on$\mathcal{C}^n$ is comparable to $n^d (\log n)^2$. Noting that the cover timefor the simple random walk on $[-n, n]^d \cap \mathbb{Z}^d$ is of order $n^d\log n$ for $d \ge 3$ (and of order $n^2 (\log n)^2$ for $d = 2$), this gives aquantitative difference between the two random walks for $d \ge 3$.

Effective resistances for supercritical percolation clusters in boxes