Constructive Matrix Theory for Higher-Order Interaction

  • Thomas Krajewski
  • Vincent RivasseauEmail author
  • Vasily Sazonov


This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this representation. It allows us to prove that the perturbation series of the free energy for such models is analytic in a domain uniform in the sizeNof the matrix.

Mathematics Subject Classification




The work of VS was supported by the FWF Austrian funding agency through the Schroedinger fellowship J-3981.

Supplementary material


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Thomas Krajewski
    • 1
  • Vincent Rivasseau
    • 2
    Email author
  • Vasily Sazonov
    • 2
  1. 1.Centre de Physique Théorique, CNRS UMR 7332Université Aix-MarseilleMarseilleFrance
  2. 2.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris-SudOrsayFrance

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