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Article Dans Une Revue Annales Henri Poincaré Année : 2019

Constructive Matrix Theory for Higher Order Interaction

Résumé

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.

Dates et versions

hal-02073627 , version 1 (20-03-2019)

Identifiants

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Thomas Krajewski, Vincent Rivasseau, Vasily Sazonov. Constructive Matrix Theory for Higher Order Interaction. Annales Henri Poincaré, 2019, 20 (12), pp.3997-4032. ⟨10.1007/s00023-019-00845-9⟩. ⟨hal-02073627⟩
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