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.
Publications and preprints
Two-point symmetrization and convexity
(with Mathieu Fradelizi), Archiv der Mathematik
82 (2004), 282-288.
A sharp small deviation inequality for the largest eigenvalue of
a random matrix, Séminaire de
probabilités (2005), volume XXXVIII (LNM 1857).
Tensor product of convex sets and the volume
of separable states on N qudits (with Stanislaw Szarek),
Physical Review A 73 (2006).
Random points in the unit ball of
\ell_p^n, Positivity 10, (2006)
Sampling convex bodies: a random matrix
Proceedings AMS 135
Catalytic majorization and \ell_p norms
(with Ion Nechita), Communications in Mathematical
Physics 278 (2008), 133-144.
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).
On almost randomizing channels with a
short Kraus decomposition,
Communications in Mathematical Physics 288, 1103-1116
Maximal inequality for high-dimensional cubes,
Confluentes Mathematici 1, 169-179 (2009).
Non-additivity of Rényi entropy and Dvoretzky's Theorem,
(with Stanislaw Szarek and Elisabeth Werner), Journal of
Mathematical Physics 51, 022102 (2010).
Hastings's additivity counterexample via Dvoretzky's theorem,
(with Stanislaw Szarek and Elisabeth Werner),
Communications in Mathematical Physics 305, 85-97 (2011)
Partial transposition of random states and non-centered semicircular
Matrices: Theory and Applications 1, 1250001 (2012).
The multiplicative property characterizes l_p and L_p norms,
(with Ion Nechita), Confluentes mathematici 3,
- 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
transitions for random states and a semi-circle law for the partial
transpose, Physical Review A (Rapid Communications)
85, 030302 (2012)
Realigning random states, (with Ion Nechita),
Journal of Mathematical Physics 53, 102210 (2012).
On the distinguishability norms in quantum information, (with Cécilia Lancien),
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