Benoît Collins

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math.PR2026

Weingarten Calculus with Virtual Isometries

BenoÃ®t Collins, Benoît Collins, Sho Matsumoto

In this paper, we develop a novel approach to the Weingarten calculus by employing the notion of virtual isometries. Traditionally, Weingarten calculus provides explicit formulas f…

math.PR2026

Smooth Multi-Trace Statistics of Classical Ensembles: Large $N$ Expansions, Cumulants, and Matrix Integrals

BenoÃ®t Collins, Manasa Nagatsu

We consider expectations of the form $E [t r h_{1} (X_{1}^{N}) ... t r h_{r} (X_{r}^{N})]$ , where $X_{i}^{N}$ are self-adjoint polynomials in various independent classical random matrices and $h_{i}$ are…

math.PR2025

Weingarten calculus for centered random permutation matrices

BenoÃ®t Collins, Manasa Nagatsu

We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S_N. After presenting a formulation of the Weingarten calculus on the…

Weingarten Calculus with Virtual Isometries

Smooth Multi-Trace Statistics of Classical Ensembles: Large N Expansions, Cumulants, and Matrix Integrals

Weingarten calculus for centered random permutation matrices

Smooth Multi-Trace Statistics of Classical Ensembles: Large $N$ Expansions, Cumulants, and Matrix Integrals