Loop Vertex Representation for Cumulants, Part II: Weingarten Calculus

2025/10/25 by Rivasseau, Vincent
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.22372

Abstract

In this paper we construct scalar cumulants for stable random matrix models with single trace interactions of arbitrarily high even order by Weingarten calculus. We obtain explicit and convergent expansions for these scalar cumulants in the limit N tend to infinity.

Citations

• Variational Loop Vertex Expansion
• Loop Vertex Representation for Cumulants, Part I: Bounds on Free Energy with Sources
• Constructive Matrix Theory for Higher Order Interaction II: Hermitian and Real Symmetric Cases
• Constructive Matrix Theory for Higher Order Interaction
• Analyticity results for the cumulants in a random matrix model
• Renormalization: an advanced overview
• Universality for Random Tensors
• Moments and Cumulants of Polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability
• A planar diagram theory for strong interactions

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• Analyticity results for the cumulants in a random matrix model
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• Constructive Matrix Theory for Higher Order Interaction