Communications in Mathematical Physics

, Volume 179, Issue 1, pp 235–256 | Cite as

Almost flat planar diagrams

  • Vladimir A. Kazakov
  • Matthias Staudacher
  • Thomas Wynter


We continue our study of matrix models of dually weighted graphs. Among the attractive features of these models is the possibility to interpolate between ensembles of regular and random two-dimensional lattices, relevant for the study of the crossover from two-dimensional flat space to two-dimensional quantum gravity. We further develop the formalism of largeN character expansions. In particular, a general method for determining the largeN limit of a character is derived. This method, aside from being potentially useful for a far greater class of problems, allows us to exactly solve the matrix models of dually weighted graphs, reducing them to a well-posed Riemann-Hilbert problem. The power of the method is illustrated by explicitly solving a new model in which only positive curvature defects are permitted on the surface, an arbitrary amount of negative curvature being introduced at a single insertion.


Attractive Feature Quantum Gravity Matrix Model Quantum Computing Weighted Graph 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Vladimir A. Kazakov
    • 1
  • Matthias Staudacher
    • 1
  • Thomas Wynter
    • 1
  1. 1.Laboratoire de Physique Théorique de l'École Normale SupérieureParis Cedex 05France

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