Constructive Matrix Theory for Higher Order Interaction

Abstract : 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 to prove that the perturbation series of the free energy for such models is analytic in a domain uniform in the size N of the matrix. Our method applies to complex (rectangular) matrices. The extension to Hermitian square matrices, which was claimed wrongly in the first arXiv version of this paper, is postponed to a future study.
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https://hal.archives-ouvertes.fr/hal-02073627
Contributor : Thomas Krajewski <>
Submitted on : Wednesday, March 20, 2019 - 9:50:12 AM
Last modification on : Friday, March 22, 2019 - 1:15:53 AM

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  • HAL Id : hal-02073627, version 1
  • ARXIV : 1712.05670

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Thomas Krajewski, Vincent Rivasseau, Vasily Sazonov. Constructive Matrix Theory for Higher Order Interaction. 2019. ⟨hal-02073627⟩

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