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
Publications and preprints
Two-point symmetrization and convexity
(with Mathieu Fradelizi), Archiv der Mathematik
82 (2004), 282-288. Pulished version.
A sharp small deviation inequality for the largest eigenvalue of
a random matrix, Séminaire de
probabilités (2005), volume XXXVIII (LNM 1857). Pulished version.
Tensor product of convex sets and the volume
of separable states on N qudits (with Stanislaw Szarek),
Physical Review A 73 (2006). Pulished version.
Random points in the unit ball of
\ell_p^n, Positivity 10, (2006)
755-759. Pulished version.
Sampling convex bodies: a random matrix
Proceedings AMS 135
(2007), 1293-1303. Pulished version.
Catalytic majorization and \ell_p norms
(with Ion Nechita), Communications in Mathematical
Physics 278 (2008), 133-144. Pulished version.
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.
On almost randomizing channels with a
short Kraus decomposition,
Communications in Mathematical Physics 288, 1103-1116
(2009). Pulished version.
Maximal inequality for high-dimensional cubes,
Confluentes Mathematici 1, 169-179 (2009). Pulished version.
Non-additivity of Rényi entropy and Dvoretzky's Theorem,
(with Stanislaw Szarek and Elisabeth Werner), Journal of
Mathematical Physics 51, 022102 (2010). Pulished version.
Hastings's additivity counterexample via Dvoretzky's theorem,
(with Stanislaw Szarek and Elisabeth Werner),
Communications in Mathematical Physics 305, 85-97 (2011). Pulished version.
Partial transposition of random states and non-centered semicircular
Matrices: Theory and Applications 1, 1250001 (2012). Pulished version.
The multiplicative property characterizes l_p and L_p norms,
(with Ion Nechita), Confluentes mathematici 3,
637 (2011). Pulished version.
- 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
Realigning random states, (with Ion Nechita),
Journal of Mathematical Physics 53, 102210 (2012). Pulished version.
Zonoids and sparsification of quantum measurements, (with Cécilia Lancien),
Positivity 20, 1-23 (2016). Pulished version.
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.
Catalysis in the trace class and weak trace class ideals, (with Fedor Sukochev and Dmitriy Zanin),
Proceedings AMS 144, 2461-2471 (2016). Pulished version.
Quantum Entanglement in high dimensions, Lecture notes from a winter school in Métabief (December 2014)
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.
Universal gaps for XOR games from estimates on tensor norm ratios, (with Ludovico Lami, Carlos Palazuelos, Stanislaw Szarek and Anreas Winter), 43p,
link to arXiv preprint.
These are notes I mostly wrote for myself, and share here in case somebody is interested.
- 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
- 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.
Here is a version(dvi
of my PhD thesis.
And there is also a curriculum vitae (dvi).
To reach me:
aubrun (arrobas) math. univ-lyon1. fr