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

This paper studies Gaussian random fields with Mat\'ern covariance functionwith smooth parameter $\nu>2$. Two cases of parameter spaces, the Euclideanspace and $N$-dimensional sphere, are considered. For such smooth Gaussianfields, we have derived the explicit formulae for the expected Eulercharacteristic of the excursion set, the expected number and heightdistribution of critical points. The results are valuable for approximating theexcursion probability and computing p-values for peak inference.

Smooth Mat\'ern Gaussian Random Fields: Euler Characteristic, Expected Number and Height Distribution of Critical Points