Félix Parraud

activity

20192025

most citedOn the operator norm of non-commutative polynomials in deterministic matrices and iid GUE matrices

17 citations · 30 across the 8 of their papers we have counts for

collaborators

9 papers

math.PR2025

Eigenvalues of Brownian Motions on $GL (N, C)$

Tatiana Brailovskaya, Nicholas A. Cook, Todd Kemp +1

We prove that the empirical law of eigenvalues of Brownian motion on the Lie Group $GL (N, C)$ converges almost surely to a deterministic probability measure, chara…

math.PR2025

Matrix Random Walks and the Lima Bean Law

Bruce K. Driver, Brian C. Hall, Ching Wei Ho +4

A matrix random walk is a stochastic process of the form $B_{k} = (I + A_{1}) \dots (I + A_{k})$ where $A_{j}$ are independent ``step'' matrices in $M_{N} (C)$ . With the right en…

math.PR2024

The spectrum of a tensor of random and deterministic matrices

Félix Parraud

We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^{p}$ -norm can be upper bounded, up to an asymptotically small error, by t…

math.PR2023

Asymptotic expansion of smooth functions in deterministic and iid Haar unitary matrices, and application to tensor products of matrices

Félix Parraud

Let $U^{N}$ be a family of $N \times N$ independent Haar unitary random matrices and their adjoints, $Z^{N}$ a family of deterministic matrices, and $P$ a self-adjoint noncommutative po…

math.OA2021★ 5 cited

Convergence for noncommutative rational functions evaluated in random matrices

Benoît Collins, Tobias Mai, Akihiro Miyagawa +2

One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ …

quant-ph2020★ 4 cited

Concentration estimates for random subspaces of a tensor product, and application to Quantum Information Theory

Benoît Collins, Félix Parraud

Given a random subspace $H_{n}$ chosen uniformly in a tensor product of Hilbert spaces $V_{n} \otimes W$ , we consider the collection $K_{n}$ of all singular values of all norm one element…

math.PR2020★ 1 cited

Asymptotic expansion of smooth functions in polynomials in deterministic matrices and iid GUE matrices

Felix Parraud

Let $X^{N}$ be a family of $N \times N$ independent GUE random matrices, $Z^{N}$ a family of deterministic matrices, $P$ a self-adjoint non-commutative polynomial, that is for any $N$ ,…

math.PR2020★ 3 cited

On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices

Félix Parraud

Let $U^{N} = (U_{1}^{N}, \dots, U_{p}^{N})$ be a d-tuple of $N \times N$ independent Haar unitary matrices and $Z^{N M}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\oti…

math.PR2019★ 17 cited

On the operator norm of non-commutative polynomials in deterministic matrices and iid GUE matrices

Benoît Collins, Alice Guionnet, Félix Parraud

Let $X^{N} = (X_{1}^{N}, \dots, X_{d}^{N})$ be a d-tuple of $N \times N$ independent GUE random matrices and $Z^{N M}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otime…

Eigenvalues of Brownian Motions on GL(N,C)

Matrix Random Walks and the Lima Bean Law

The spectrum of a tensor of random and deterministic matrices

Asymptotic expansion of smooth functions in deterministic and iid Haar unitary matrices, and application to tensor products of matrices

Convergence for noncommutative rational functions evaluated in random matrices

Concentration estimates for random subspaces of a tensor product, and application to Quantum Information Theory

Asymptotic expansion of smooth functions in polynomials in deterministic matrices and iid GUE matrices

On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices

On the operator norm of non-commutative polynomials in deterministic matrices and iid GUE matrices

Eigenvalues of Brownian Motions on $GL (N, C)$