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

For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in K}$ whichis invariant, in law, under unitary conjugation, we give general sufficientconditions for central limit theorems for random variables of the type$\operatorname{Tr}(\mathbf{A}_k \mathbf{M})$, where the matrix $\mathbf{M}$ isdeterministic (such random variables include for example the normalized matrixentries of the $\mathbf{A}_k$'s). A consequence is the asymptotic independenceof the projection of the matrices $\mathbf{A}_k$ onto the subspace of nulltrace matrices from their projections onto the orthogonal of this subspace.These results are used to study the asymptotic behavior of the outliers of aspiked elliptic random matrix. More precisely, we show that the fluctuations ofthese outliers around their limits can have various rates of convergence,depending on the Jordan Canonical Form of the additive perturbation. Also, somecorrelations can arise between outliers at a macroscopic distance from eachother. These phenomena have already been observed by Benaych-Georges and Rochetwith random matrices from the Single Ring Theorem.

Fluctuation of matrix entries and application to outliers of elliptic matrices