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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper studies the almost sure location of the eigenvalues of matrices${\bf W}_N {\bf W}_N^{*}$ where ${\bf W}_N = ({\bf W}_N^{(1)T}, ..., {\bfW}_N^{(M)T})^{T}$ is a $ML \times N$ block-line matrix whose block-lines $({\bfW}_N^{(m)})_{m=1, ..., M}$ are independent identically distributed $L \times N$Hankel matrices built from i.i.d. standard complex Gaussian sequences. It isshown that if $M \rightarrow +\infty$ and $\frac{ML}{N} \rightarrow c_*$ ($c_*\in (0, \infty)$), then the empirical eigenvalue distribution of ${\bf W}_N{\bf W}_N^{*}$ converges almost surely towards the Marcenko-Pasturdistribution. More importantly, it is established that if $L =\mathcal{O}(N^{\alpha})$ with $\alpha < 2/3$, then, almost surely, for $N$large enough, the eigenvalues of ${\bf W}_N {\bf W}_N^{*}$ are located in theneighbourhood of the Marcenko-Pastur distribution.

On the almost sure location of the singular values of certain Gaussian block-Hankel large random matrices