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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider $n\times n$ Hermitian matrices with i.i.d. entries $X_{ij}$ whosetail probabilities $\mathbb {P}(|X_{ij}|\geq t)$ behave like $e^{-at^{\alpha}}$for some $a>0$ and $\alpha \in(0,2)$. We establish a large deviation principlefor the empirical spectral measure of $X/\sqrt{n}$ with speed $n^{1+\alpha /2}$with a good rate function $J(\mu)$ that is finite only if $\mu$ is of the form$\mu=\mu_{\mathrm{sc}}\boxplus\nu$ for some probability measure $\nu$ on$\mathbb {R}$, where $\boxplus$ denotes the free convolution and$\mu_{\mathrm{sc}}$ is Wigner's semicircle law. We obtain explicit expressionsfor $J(\mu_{\mathrm{sc}}\boxplus\nu)$ in terms of the $\alpha$th moment of$\nu$. The proof is based on the analysis of large deviations for the empiricaldistribution of very sparse random rooted networks.

A large deviation principle for Wigner matrices without Gaussian tails