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

We prove that the set of $\gamma$-thick points of a planar Gaussian freefield (GFF) with Dirichlet boundary conditions is a.s. totally disconnected forall $\gamma \neq 0$. Our proof relies on the coupling between a GFF and thenested CLE$_4$. In particular, we show that the thick points of the GFF are thesame as those of the weighted CLE$_4$ nesting field and establish the almostsure total disconnectedness of the complement of a nested CLE$_{\kappa}$,$\kappa \in (8/3,4]$. As a corollary we see that the set of singular points forsupercritical LQG metrics is a.s. totally disconnected.

Thick points of the planar GFF are totally disconnected for all $\gamma\ne 0$