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

We present a method to derive asymptotics of eigenvalues for trace-classintegral operators $K:L^2(J;d\lambda)\circlearrowleft$, acting on a singleinterval $J\subset\mathbb{R}$, which belong to the ring of integrable operators\cite{IIKS}. Our emphasis lies on the behavior of the spectrum$\{\lambda_i(J)\}_{i=0}^{\infty}$ of $K$ as $|J|\rightarrow\infty$ and $i$ isfixed. We show that this behavior is intimately linked to the analysis of theFredholm determinant $\det(I-\gamma K)|_{L^2(J)}$ as $|J|\rightarrow\infty$ and$\gamma\uparrow 1$ in a Stokes type scaling regime. Concrete asymptoticformul\ae\, are obtained for the eigenvalues of Airy and Bessel kernels inrandom matrix theory.

From gap probabilities in random matrix theory to eigenvalue expansions