Loop Vertex Representation for Cumulants, Part II: Weingarten Calculus

TL;DR

This paper develops a method using Weingarten calculus to compute scalar cumulants for stable random matrix models with high-order interactions, providing explicit formulas and convergence results as matrix size grows.

Contribution

It introduces a novel application of Weingarten calculus to construct and analyze scalar cumulants in complex random matrix models with high-order interactions.

Findings

Explicit convergent expansions for scalar cumulants as N approaches infinity.

Application of Weingarten calculus to high-order single trace interactions.

Framework for analyzing stable random matrix models with complex interactions.

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.