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 $R_n$ be the range of a critical branching random walk with $n$ particleson $\mathbb Z^d$, which is the set of sites visited by a random walk indexed bya critical Galton--Watson tree conditioned on having exactly $n$ vertices. For$d\in\{3, 4, 5\}$, we prove that $n^{-\frac{d-2}4} \mathtt{cap}^{(d)}(R_n)$,the renormalized capacity of $R_n$, converges in law to the capacity of thesupport of the integrated super-Brownian excursion. The proof relies on a studyof the intersection probabilities between the critical branching random walkand an independent simple random walk on $\mathbb Z^d$.

Convergence in law for the capacity of the range of a critical branching random walk