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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study (asymmetric) $U$-statistics based on a stationary sequence of$m$-dependent variables; moreover, we consider constrained $U$-statistics,where the defining multiple sum only includes terms satisfying somerestrictions on the gaps between indices. Results include a law of largenumbers and a central limit theorem. Special attention is paid to degeneratecases where, after the standard normalization, the asymptotic variancevanishes; in these cases non-normal limits occur after a differentnormalization.  The results are motivated by applications to pattern matching in randomstrings and permutations. We obtain both new results and new proofs of oldresults.

Asymptotic normality for $m$-dependent and constrained $U$-statistics, with applications to pattern matching in random strings and permutations