The Anti-Symmetric GUE Minor Process

Understand

Our study is initiated by a multi-component particle system underlying the tiling of a half hexagon by three species of rhombi.

• In this particle system species $j$ consists of $\lfloor j/2 \rfloor$ particles which are interlaced with neigbouring species.
• The joint probability density function (PDF) for this particle system is obtained, and is shown in a suitable scaling limit to coincide with the joint eigenvalue PDF for the process formed by the successive minors of anti-symmetric GUE matrices, which in turn we compute from first principles.
• The correlations for this process are determinantal and we give an explicit formula for the corresponding correlation kernel in terms of Hermite polynomials.