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Félix Parraud


Contact Info:

Queen's university,
48 University Ave, Jeffery Hall,
ON K7L 3N8, Kingston, Canada.

Office: Jeffery Hall, 515.
Email: felix.parraud@gmail.com

About me:

I am currently a Postdoctoral Fellow in the Department of Mathematics & Statistics of Queen's university under the supervision of James Mingo.

Previously, I was a postdoc with Kevin Schnelli in the group Random matrices, Stochastic Models and Analysis at KTH Royal Institute of Technology. I obtained my Ph.D. degree in 2021 from ENS Lyon and Kyoto University, under the cosupervision of Alice Guionnet and Benoît Collins. I received my master degree in mathematics from ENS Lyon in 2017.

My research interests are in Random Matrix Theory and Free Probability.

I have notably been working on a strategy to interpolate random matrices with free operators, this is the main technical tool of several of the papers listed below. You can find here an elementary introduction to the topic.

Publications and preprints:

  1. The spectrum of a tensor of random and deterministic matrices ,
    preprint (2024).

  2. The free energy of matrix models ,
    with Kevin Schnelli,
    preprint (2023).

  3. Asymptotic expansion of smooth functions in deterministic and iid Haar unitary matrices, and application to tensor products of matrices,
    preprint (2023).

  4. Asymptotic freeness through unitaries generated by polynomials of Wigner matrices,
    with Kevin Schnelli,
    Linear Algebra and its Applications (2024, originally announced in 2022).

  5. Convergence for noncommutative rational functions evaluated in random matrices,
    with Benoît Collins, Tobias Mai, Akihiro Miyagawa and Sheng Yin,
    Mathematische Annalen (2022, originally announced in 2021), 1-32.

  6. Concentration estimates for random subspaces of a tensor product and application to quantum information theory,
    with Benoît Collins,
    Journal of Mathematical Physics (2022, originally announced in 2020), 63(10), 102202.

  7. Asymptotic expansion of smooth functions in polynomials in deterministic matrices and iid GUE matrices,
    Communications in Mathematical Physics (2023, originally announced in 2020), 399(1), 249-294.

  8. On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices,
    Probability Theory and Related Fields (2022, originally announced in 2020), 182(3-4), 751-806.

  9. On the operator norm of non-commutative polynomials in deterministic matrices and iid GUE matrices,
    with Benoît Collins and Alice Guionnet,
    Cambridge Journal of Mathematics (2022, originally announced in 2019), 10(1), 195-260.

Last updated : February 13, 2025.