Areas of interest

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.

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.
2. A sharp small deviation inequality for the largest eigenvalue of a random matrix, Séminaire de probabilités (2005), volume XXXVIII (LNM 1857).
3. Tensor product of convex sets and the volume of separable states on N qudits (with Stanislaw Szarek), Physical Review A 73 (2006).
4. Random points in the unit ball of \ell_p^n, Positivity 10, (2006) 755-759.
5. Sampling convex bodies: a random matrix approach, Proceedings AMS 135 (2007), 1293-1303.
6. Catalytic majorization and \ell_p norms (with Ion Nechita), Communications in Mathematical Physics 278 (2008), 133-144.
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).
8. On almost randomizing channels with a short Kraus decomposition, Communications in Mathematical Physics 288, 1103-1116 (2009).
9. Maximal inequality for high-dimensional cubes, Confluentes Mathematici 1, 169-179 (2009).
10. Non-additivity of Rényi entropy and Dvoretzky's Theorem, (with Stanislaw Szarek and Elisabeth Werner), Journal of Mathematical Physics 51, 022102 (2010).
11. Hastings's additivity counterexample via Dvoretzky's theorem, (with Stanislaw Szarek and Elisabeth Werner), Communications in Mathematical Physics 305, 85-97 (2011)
12. Partial transposition of random states and non-centered semicircular distributions, Random Matrices: Theory and Applications 1, 1250001 (2012).
13. The multiplicative property characterizes l_p and L_p norms, (with Ion Nechita), Confluentes mathematici 3, 637 (2011).
14. Entanglement thresholds for random induced states, (with Stanislaw Szarek and Deping Ye), Communications in Pure and Applied Mathematics 67, 129-171 (2013?) ; 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) 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).
16. Zonoids and sparsification of quantum measurements, (with Cécilia Lancien), to appear in Positivity (2015?).
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).
18. Catalysis in the trace class and weak trace class ideals, (with Fedor Sukochev and Dmitriy Zanin), to appears in Proceedigs AMS (2015?).
19. Dvoretzky's theorem and the complexity of entanglement detection, (with Stanislaw Szarek), preprint.

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