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/

Zendy Plus

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

Zendy Tools

Zendy Open

Place an obstacle with probability $1-p$ independently at each vertex of$\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles.For $d\geq 2$ and $p$ strictly above the critical threshold for sitepercolation, we condition on the environment where the origin is contained inan infinite connected component free of obstacles, and we show that forenvironments with probability tending to one as $n\to \infty$ there exists aunique discrete Euclidean ball of volume $d \log_{1/p} n$ asymptotically suchthat the following holds: conditioned on survival up to time $n$ we have thatat any time $t \in [o(n),n]$ with probability tending to one the simple randomwalk is in this ball. This work relies on and substantially improves a previousresult of the authors on localization in a region of volume poly-logarithmic in$n$ for the same problem.

Localization for random walks among random obstacles in a single Euclidean ball