The Anti-Symmetric GUE Minor Process
2009 (English)In: Moscow Mathematical Journal, ISSN 1609-3321, Vol. 9, no 4, 749-774 p.Article in journal (Refereed) Published
Our study is initiated by a multi-component particle system underlyingthe tiling of a half hexagon by three species of rhombi. In this particlesystem species $j$ consists of $\lfloor j/2 \rfloor$ particles which areinterlaced with neigbouring species. The joint probability densityfunction (PDF) for this particle system is obtained, and is shown in asuitable scaling limit to coincide with the joint eigenvalue PDFfor the process formed by the successive minors of anti-symmetric GUEmatrices, which in turn we compute from first principles. The correlationsfor this process are determinantal and we give an explicit formula for thecorresponding correlation kernel in terms of Hermite polynomials.Scaling limits of the latter are computed, giving rise to theAiry kernel, extended Airy kernel and bead kernel at the soft edge and inthe bulk, as well as a new kernel at the hard edge.
Place, publisher, year, edition, pages
2009. Vol. 9, no 4, 749-774 p.
Anti-symmetric GUE, lozenge tilings, interlaced particles
IdentifiersURN: urn:nbn:se:kth:diva-9831ISI: 000273089600002OAI: oai:DiVA.org:kth-9831DiVA: diva2:133479
QC 201008042009-01-192009-01-122011-07-06Bibliographically approved