I'm interested in the following topics

• Convex geometry, especially high-dimensional. This field is sometimes called Asymptotic Geometric Analysis.
• Quantum information theory and its interplay with the former.
• Random matrices.

Book

Alice and Bob meet Banach (book written with Stanislaw Szarek)

Publications and preprints

1. Two-point symmetrization and convexity (with Mathieu Fradelizi), Archiv der Mathematik 82 (2004), 282-288. Pulished version.
2. A sharp small deviation inequality for the largest eigenvalue of a random matrix, Séminaire de probabilités (2005), volume XXXVIII (LNM 1857). Pulished version.
3. Tensor product of convex sets and the volume of separable states on N qudits (with Stanislaw Szarek), Physical Review A 73 (2006). Pulished version.
4. Random points in the unit ball of \ell_p^n, Positivity 10, (2006) 755-759. Pulished version.
5. Sampling convex bodies: a random matrix approach, Proceedings AMS 135 (2007), 1293-1303. Pulished version.
6. Catalytic majorization and \ell_p norms (with Ion Nechita), Communications in Mathematical Physics 278 (2008), 133-144. Pulished version.
7. Stochastic ordering for iterated convolutions and catalytic majorization (with Ion Nechita), Annales de l'Institut Henri Poincaré (probabilité et statistiques) 45 (3), 611-625 (2009). Pulished version.
8. On almost randomizing channels with a short Kraus decomposition, Communications in Mathematical Physics 288, 1103-1116 (2009). Pulished version.
9. Maximal inequality for high-dimensional cubes, Confluentes Mathematici 1, 169-179 (2009). Pulished version.
10. Non-additivity of Rényi entropy and Dvoretzky's Theorem, (with Stanislaw Szarek and Elisabeth Werner), Journal of Mathematical Physics 51, 022102 (2010). Pulished version.
11. Hastings's additivity counterexample via Dvoretzky's theorem, (with Stanislaw Szarek and Elisabeth Werner), Communications in Mathematical Physics 305, 85-97 (2011). Pulished version.
12. Partial transposition of random states and non-centered semicircular distributions, Random Matrices: Theory and Applications 1, 1250001 (2012). Pulished version.
13. The multiplicative property characterizes l_p and L_p norms, (with Ion Nechita), Confluentes mathematici 3, 637 (2011). Pulished version.
14. Entanglement thresholds for random induced states, (with Stanislaw Szarek and Deping Ye), Communications in Pure and Applied Mathematics 67, 129-171 (2014) Pulished version. ; see also the non-technical overview Phase transitions for random states and a semi-circle law for the partial transpose, Physical Review A (Rapid Communications) 85, 030302 (2012) Pulished version. and the proceeding from ICMP 2012: Is a random state entangled?
15. Realigning random states, (with Ion Nechita), Journal of Mathematical Physics 53, 102210 (2012). Pulished version.
16. Zonoids and sparsification of quantum measurements, (with Cécilia Lancien), Positivity 20, 1-23 (2016). Pulished version.
17. Locally restricted measurements on a multipartite quantum system: data hiding is generic, (with Cécilia Lancien), Quantum Information and Computation 15, no. 5-6, 513--540. (2015). Pulished version.
18. Catalysis in the trace class and weak trace class ideals, (with Fedor Sukochev and Dmitriy Zanin), Proceedings AMS 144, 2461-2471 (2016). Pulished version.
19. Quantum Entanglement in high dimensions, Lecture notes from a winter school in Métabief (December 2014) preliminary version.
20. Dvoretzky's theorem and the complexity of entanglement detection, (with Stanislaw Szarek), accepted for QIP'16. Discrete Analysis 1, 20pp (2017), Editorial introduction with link to arXiv version.
21. Universal gaps for XOR games from estimates on tensor norm ratios, (with Ludovico Lami, Carlos Palazuelos, Stanislaw Szarek and Andreas Winter), Communications in Mathematical Physics 375 (2020), 679-724, link to arXiv preprint.
22. Entangleability of cones, (with Ludovico Lami, Carlos Palazuelos and Martin Plávala), Geometric and Functional Analysis 31 (2021), 181-205, link to arXiv preprint. Here is a video of a talk I gave at QPL'21.
23. Entanglement and superposition are equivalent concepts in any physical theory (with Ludovico Lami, Carlos Palazuelos and Martin Plávala), Physical Review Letters 128 160402 (2022), link to arXiv preprint. This essentially subsumes the earlier prerpint "Universal entangleability of non-classical theories"
24. Principal angles between random subspaces and polynomials in two free projections, Confluentes Mathematici 13 (2021), n°2, 3-10 link to journal version.
25. Annihilating Entanglement Between Cones (with Alexander Müller-Hermes), Communications in Mathematical Physic 400, 931-976 (2023), link to arXiv preprint.
26. Asymptotic Tensor Powers of Banach Spaces (with Alexander Müller-Hermes), link to arXiv preprint.
27. Vers la conjecture de Kannan-Lovász-Simonovits, d'après Yuansi Chen, séminaire Bourbaki, exposé n°1192 (Astérisque, 2022), pdf version (in French)
28. Monogamy of entanglement between cones (with Alexander Müller-Hermes and Martin Plávala), link to arXiv preprint.
29. Maximal exponent of the Lorentz cones (with Jing Bai), link to arXiv preprint.
30. Completely Bounded Norms of k-positive Maps (with Kenneth Davidson, Alexander Müller-Hermes, Vern Paulsen and Mizanur Rahaman), link to arXiv preprint

1. A naive look at Schur-Weyl duality (Sep. 2018). An elementary proof (no representation theory) of easy versions of Schur-Weyl duality which appear in quantum information theory.
2. Convex bodies with a dense projective orbit (Dec. 2018). There is a convex body with the property that the set of its projective images is dense in the set of convex bodies.
3. The parallel repetition theorem (Dec. 2021). This is my own writing of the proof (by Holenstein) of Ran Raz' parallel repetition theorem.

Here is a version(dvi ps pdf) of my PhD thesis.

And there is also a curriculum vitae (dvi).

To reach me:
aubrun (arrobas) math. univ-lyon1. fr

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