1997/02/28 by Gernot Akemann · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Arc (geometry) #Eigenvalues and eigenvectors #Geometry #Hermitian matrix #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix model #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Scaling #Scaling limit #String (physics) #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00552-x
published as Nucl.Phys. B507 (1997) 475-500 · 25 pages, LaTex, minor changes, to appear in Nucl.Phys.B
arxiv created 1997/08/15 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and hermitian model.