39 citations · 66 across the 9 of their papers we have counts for
13 papers
Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices
Serban Belinschi, Charles Bordenave, Mireille Capitaine +1
We consider a square random matrix of size of the form where is a noncommutative polynomial, is a tuple of deterministic matrices converging in -distribu…
A note on existence of free Stein kernels
Guillaume Cébron, Max Fathi, Tobias Mai
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is…
Operator-Valued Matrices with Free or Exchangeable Entries
Marwa Banna, Guillaume Cébron
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial -probability space. More precisely, we consider operator-valued Wigner and Wis…
Large permutation invariant random matrices are asymptotically free over the diagonal
Benson Au, Guillaume Cébron, Antoine Dahlqvist +2
We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform bound…
A quantitative fourth moment theorem in free probability theory
Guillaume Cébron
A quantitative "fourth moment theorem" is provided for any self-adjoint element in a homogeneous Wigner chaos: the Wasserstein distance is controlled by the distance from the fourt…
Quantum groups based on spatial partitions
Guillaume Cébron, Moritz Weber
We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This ext…
Fluctuation of matrix entries and application to outliers of elliptic matrices
Florent Benaych-Georges, Guillaume Cébron, Jean Rochet
For any family of random matrices which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central lim…
The generalized master fields
Guillaume Cébron, Antoine Dahlqvist, Franck Gabriel
The master field is the large limit of the Yang-Mills measure on the Euclidean plane. It can be viewed as a non-commutative process indexed by paths on the plane. We construct…
Traffic Distributions and Independence II: Universal Constructions for Traffic Spaces
Guillaume Cébron, Antoine Dahlqvist, Camille Male
We investigate questions related to the notion of traffics introduced by the author C. Male as a noncommutative probability space with numerous additional operations and equipped w…
Haar states and Lévy processes on the unitary dual group
Guillaume Cébron, Michaël Ulrich
We study states on the universal noncommutative *-algebra generated by the coefficients of a unitary matrix, or equivalently states on the unitary dual group. Its structure of dual…
Fluctuations of Brownian Motions on GL_N
Guillaume Cébron, Todd Kemp
We consider a two parameter family of unitarily invariant diffusion processes on the general linear group of invertible matrices, that includes the stan…
Matricial model for the free multiplicative convolution
Guillaume Cébron
This paper investigates homomorphisms à la Bercovici-Pata between additive and multiplicative convolutions. We also consider their matricial versions which are associated with meas…
Free Convolution Operators and Free Hall Transform
Guillaume Cébron
We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transi…