2011/05/31 by Olivier Marchal, O Marchal
Computer Science · Mathematics · Physics and Astronomy · #Context (archaeology) #Eigenvalues and eigenvectors #Hermitian matrix #Limiting #Matrix (chemical analysis) #Matrix Theory and Algorithms #Parametrization (atmospheric modeling) #Quantum Mechanics and Non-Hermitian Physics #Random Matrices and Applications #Recursion (computer science) #Set (abstract data type) #String (physics) #hep-th #math-ph #math.MP #math.PR #nlin.SI
paper · pdf · doi:10.1088/1742-5468/2012/01/p01011
27 pages, 2 figures. Version 2: published version in JStat. Typos fixed. Some parts have been slighly modified as suggested by the unknown referee
arxiv created 2011/12/15 · openalex publication_date 2012/01/16 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper, we study in detail the modified topological recursion of the one-matrix model for arbitrary β in the one-cut case.We show that, for polynomial potentials, the recursion can be computed as a sum of residues.However, the main difference with the Hermitian matrix model is that the residues cannot be set at the branch points of the spectral curve but require the knowledge of the whole curve.In order to establish non-ambiguous formulae, we place ourselves in the context of the globalizing parameterization which is specific to the one-cut case (also known as Zhukovsky parameterization).This situation is particularly interesting for applications since in most cases the potentials of the matrix models only have one cut in string theory.Finally, the paper exhibits some numerical simulations of histograms of the limiting density of eigenvalues for different values of the parameter β.