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arXiv · 1712.05670

Constructive Matrix Theory for Higher Order Interaction

Thomas Krajewski·Vincent Rivasseau·Vasily Sazonov
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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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Thomas Krajewski, Vincent Rivasseau, Vasily Sazonov. 2017-12-15. Constructive Matrix Theory for Higher Order Interaction. https://arxiv.org/abs/1712.05670

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