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

Non-Hermitian random matrices with symplectic symmetry provide examples forPfaffian point processes in the complex plane. These point processes arecharacterised by a matrix valued kernel of skew-orthogonal polynomials. Wedevelop their theory in providing an explicit construction of skew-orthogonalpolynomials in terms of orthogonal polynomials that satisfy a three-termrecurrence relation, for general weight functions in the complex plane. Newexamples for symplectic ensembles are provided, based on recent developments inorthogonal polynomials on planar domains or curves in the complex plane.Furthermore, Bergman-like kernels of skew-orthogonal Hermite and Laguerrepolynomials are derived, from which the conjectured universality of theelliptic symplectic Ginibre ensemble and its chiral partner follow in the limitof strong non-Hermiticity at the origin. A Christoffel perturbation ofskew-orthogonal polynomials as it appears in applications to quantum fieldtheory is provided.

Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels