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

We consider a random bistochastic matrix of size $n$ of the form $M Q$ where$M$ is a uniformly distributed permutation matrix and $Q$ is a givenbistochastic matrix. Under mild sparsity and regularity assumptions on $Q$, weprove that the second largest eigenvalue of $MQ$ is essentially bounded by thenormalized Hilbert-Schmidt norm of $Q$ when $n$ grows large. We apply thisresult to random walks on random regular digraphs and to shuffle-and-fold mapsof the unit interval popularized in fluid mixing protocols.

Spectral gap of sparse bistochastic matrices with exchangeable rows with application to shuffle-and-fold maps