7 papers
Rank-One HCIZ Integrals and Multiplicative Convolutions
Benoît Collins, Nicolas Delporte, Manasa Nagatsu +1
We study how spectral averaging interacts with the logarithm in large-dimensional rank-one Harish-Chandra--Itzykson--Zuber (HCIZ) integrals. For independent bi-unitarily invariant…
Smooth Multi-Trace Statistics of Classical Ensembles: Large Expansions, Cumulants, and Matrix Integrals
Benoît Collins, Manasa Nagatsu
We consider expectations of the form , where are self-adjoint polynomials in various independent classical random matrices and are…
Weingarten Calculus with Virtual Isometries
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…
Weingarten calculus for centered random permutation matrices
Benoît 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…
Free cumulants and freeness for unitarily invariant random tensors
Benoit Collins, Razvan Gurau, Luca Lionni
We address the question of the asymptotic description of random tensors that are local-unitary invariant, that is, invariant by conjugation by tensor products of independent unitar…
Strong convergence for tensor GUE random matrices
Benoît Collins, Wangjun Yuan
Haagerup and Thorbjørnsen proved that iid GUEs converge strongly to free semicircular elements as the dimension grows to infinity. Motivated by considerations from quantum physics…
Fluctuations of eigenvalues of a polynomial on Haar unitary and finite rank matrices
Benoît Collins, Katsunori Fujie, Takahiro Hasebe +2
This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can…