@article{AIHPB_2007__43_1_87_0,
author = {Gu\'edon, O. and Paouris, G.},
title = {Concentration of mass on the Schatten classes},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {43},
year = {2007},
pages = {87-99},
doi = {10.1016/j.anihpb.2006.01.002},
mrnumber = {2288271},
zbl = {1115.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_1_87_0}
}
Guédon, O.; Paouris, G. Concentration of mass on the Schatten classes. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 87-99. doi : 10.1016/j.anihpb.2006.01.002. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_1_87_0/
[1] , -estimate for the Euclidean norm on a convex body in isotropic position, in: Geometric Aspects of Functional Analysis (Israel, 1992-1994), Birkhäuser, Basel, 1995, pp. 1-4. | Zbl 0834.52004
[2] , , , The central limit problem for convex bodies, Trans. Amer. Math. Soc. 355 (12) (2003) 4723-4735. | MR 1997580 | Zbl 1033.52003
[3] , Jacobi polynomials associated with Selberg integrals, SIAM J. Math. Anal. 18 (2) (1987) 545-549. | MR 876291 | Zbl 0639.33001
[4] G. Aubrun, S. Szarek, Tensor products of convex sets and the volume of separable states on N qudits, Preprint.
[5] , , On convex bodies and log-concave probability measures with unconditional basis, in: , (Eds.), Geom. Aspects of Funct. Analysis, Lecture Notes in Math., vol. 1807, Springer, 2003, pp. 44-52. | MR 2083388 | Zbl 1039.52003
[6] , Complements of Lyapunov's inequality, Math. Ann. 205 (1973) 323-331. | MR 323977 | Zbl 0248.26011
[7] , , New volume ratio properties for convex symmetric bodies in , Invent. Math. 88 (2) (1987) 319-340. | MR 880954 | Zbl 0617.52006
[8] , , Distributional and norm inequalities for polynomials over convex bodies in , Math. Res. Lett. 8 (2001) 233-248. | MR 1839474 | Zbl 0989.26010
[9] , Séries de variables aléatoires gaussiennes à valeurs dans . Application aux produits d’espaces de Wiener abstraits, in: Séminaire sur la Géométrie des Espaces de Banach (1977-1978) Exp. 19, École Polytech., Palaiseau, 1978, pp. 15. | Numdam | Zbl 0395.60004
[10] , , Local operator theory, random matrices and Banach spaces, in: Handbook of the Geometry of Banach Spaces, vol. 2, North-Holland, Amsterdam, 2003, pp. 1819-1820. | MR 1999610 | Zbl 1067.46008
[11] , , , The isotropy constants of the Schatten classes are bounded, Math. Ann. 312 (1998) 773-783. | MR 1660231 | Zbl 0927.46014
[12] , Random Matrices, second ed., Academic Press, Boston, 1991. | MR 1083764 | Zbl 0780.60014
[13] , , Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, in: , (Eds.), Geom. Aspects of Funct. Analysis, Lecture Notes in Math., vol. 1376, Springer, 1989, pp. 64-104. | MR 1008717 | Zbl 0679.46012
[14] , , Asymptotic Theory of Finite-Dimensional Normed Spaces, Lecture Notes in Math., vol. 1200, Springer, Berlin, 1986. | MR 856576 | Zbl 0606.46013
[15] , Concentration of mass and central limit properties of isotropic convex bodies, Proc. Amer. Math. Soc. 133 (2005) 565-575. | MR 2093081 | Zbl 1064.52005
[16] , The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracks in Math., vol. 94, Cambridge Univ. Press, 1989. | MR 1036275 | Zbl 0698.46008
[17] , Le volume des idéaux d'opérateurs classiques, Studia Math. 80 (1984) 63-75. | MR 781729 | Zbl 0507.51015