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

Let B n = (1/N)T 1/2 n X n X* n T n 1/2 where X n is n × N with i.i.d. complex standardized entries having finite fourth moment, and T n 1/2 is a Hermitian square root of the nonnegative definite Hermitian matrix T n . It was shown in an earlier paper by the authors that, under certain conditions on the eigenvalues of T n , with probability 1 no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution (known to exist) for all large n. For these n the interval corresponds to one that separates the eigenvalues of T n . The aim of the present paper is to prove exact separation of eigenvalues; that is, with probability 1, the number of eigenvalues of B u and T n lying on one side of their respective intervals are identical for all large n.

Exact Separation of Eigenvalues of Large Dimensional Sample Covariance Matrices