Concentration of mass on the Schatten classes

Guédon, O.; Paouris, G.

doi:10.1016/j.anihpb.2006.01.002

Guédon, O. ; Paouris, G.

Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 1, pp. 87-99.

MR Zbl

DOI : 10.1016/j.anihpb.2006.01.002

@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},
     pages = {87--99},
     publisher = {Elsevier},
     volume = {43},
     number = {1},
     year = {2007},
     doi = {10.1016/j.anihpb.2006.01.002},
     mrnumber = {2288271},
     zbl = {1115.46006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2006.01.002/}
}

TY  - JOUR
AU  - Guédon, O.
AU  - Paouris, G.
TI  - Concentration of mass on the Schatten classes
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 87
EP  - 99
VL  - 43
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2006.01.002/
DO  - 10.1016/j.anihpb.2006.01.002
LA  - en
ID  - AIHPB_2007__43_1_87_0
ER  -

%0 Journal Article
%A Guédon, O.
%A Paouris, G.
%T Concentration of mass on the Schatten classes
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 87-99
%V 43
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpb.2006.01.002/
%R 10.1016/j.anihpb.2006.01.002
%G en
%F 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) no. 1, pp. 87-99. doi : 10.1016/j.anihpb.2006.01.002. http://www.numdam.org/articles/10.1016/j.anihpb.2006.01.002/

Bibliographie
Cité par

[1] S. Alesker, $ψ_{2}$ -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

[2] M. Anttila, K. Ball, I. Perissinaki, The central limit problem for convex bodies, Trans. Amer. Math. Soc. 355 (12) (2003) 4723-4735. | MR | Zbl

[3] K. Aomoto, Jacobi polynomials associated with Selberg integrals, SIAM J. Math. Anal. 18 (2) (1987) 545-549. | MR | Zbl

[4] G. Aubrun, S. Szarek, Tensor products of convex sets and the volume of separable states on N qudits, Preprint.

[5] S.G. Bobkov, F.L. Nazarov, On convex bodies and log-concave probability measures with unconditional basis, in: Milman V.D., Schechtman G. (Eds.), Geom. Aspects of Funct. Analysis, Lecture Notes in Math., vol. 1807, Springer, 2003, pp. 44-52. | MR | Zbl

[6] C. Borell, Complements of Lyapunov's inequality, Math. Ann. 205 (1973) 323-331. | MR | Zbl

[7] J. Bourgain, V.D. Milman, New volume ratio properties for convex symmetric bodies in $R^{n}$ , Invent. Math. 88 (2) (1987) 319-340. | MR | Zbl

[8] A. Carbery, J. Wright, Distributional and $L^{q}$ norm inequalities for polynomials over convex bodies in $R^{n}$ , Math. Res. Lett. 8 (2001) 233-248. | MR | Zbl

[9] S. Chevet, Séries de variables aléatoires gaussiennes à valeurs dans $E {\hat{\otimes}}_{ϵ} F$ . 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

[10] K.R. Davidson, S.J. Szarek, 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 | Zbl

[11] H. König, M. Meyer, A. Pajor, The isotropy constants of the Schatten classes are bounded, Math. Ann. 312 (1998) 773-783. | MR | Zbl

[12] M.L. Mehta, Random Matrices, second ed., Academic Press, Boston, 1991. | MR | Zbl

[13] V.D. Milman, A. Pajor, Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, in: Lindenstrauss J., Milman V.D. (Eds.), Geom. Aspects of Funct. Analysis, Lecture Notes in Math., vol. 1376, Springer, 1989, pp. 64-104. | MR | Zbl

[14] V.D. Milman, G. Schechtman, Asymptotic Theory of Finite-Dimensional Normed Spaces, Lecture Notes in Math., vol. 1200, Springer, Berlin, 1986. | MR | Zbl

[15] G. Paouris, Concentration of mass and central limit properties of isotropic convex bodies, Proc. Amer. Math. Soc. 133 (2005) 565-575. | MR | Zbl

[16] G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracks in Math., vol. 94, Cambridge Univ. Press, 1989. | MR | Zbl

[17] J. Saint-Raymond, Le volume des idéaux d'opérateurs classiques, Studia Math. 80 (1984) 63-75. | MR | Zbl

Cité par Sources :