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 explore the boundaries of sine kernel universality for the eigenvalues ofGaussian perturbations of large deterministic Hermitian matrices. Equivalently,we study for deterministic initial data the time after which Dyson's Brownianmotion exhibits sine kernel correlations. We explicitly describe this time spanin terms of the limiting density and rigidity of the initial points. Our mainfocus lies on cases where the initial density vanishes at an interior point ofthe support. We show that the time to reach universality becomes larger if thedensity vanishes faster or if the initial points show less rigidity.

Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices