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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We consider the 2-dimensional Toda lattice tau functions$\tau_n(t,s;\eta,\theta)$ deforming the probabilities $\tau_n(\eta,\theta)$that a randomly chosen matrix from the unitary group U(n), for the Haarmeasure, has no eigenvalues within an arc $(\eta,\theta)$ of the unit circle.We show that these tau functions satisfy a centerless Virasoro algebra ofconstraints, with a boundary part in the sense of Adler, Shiota and vanMoerbeke. As an application, we obtain a new derivation of a differentialequation due to Tracy and Widom, satisfied by these probabilities, linking itto the Painleve VI equation.

A centerless representation of the Virasoro algebra associated with the unitary circular ensemble