Concentration of mass on the Schatten classes
Annales de l'I.H.P. Probabilités et statistiques (2007)
- Volume: 43, Issue: 1, page 87-99
- ISSN: 0246-0203
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topGuédon, O., and Paouris, G.. "Concentration of mass on the Schatten classes." Annales de l'I.H.P. Probabilités et statistiques 43.1 (2007): 87-99. <http://eudml.org/doc/77926>.
@article{Guédon2007,
author = {Guédon, O., Paouris, G.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Schatten-von Neumann classes; isotropic measure; Kahane-Khinchine inequalities; concentration inequalities},
language = {eng},
number = {1},
pages = {87-99},
publisher = {Elsevier},
title = {Concentration of mass on the Schatten classes},
url = {http://eudml.org/doc/77926},
volume = {43},
year = {2007},
}
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
PB - Elsevier
VL - 43
IS - 1
SP - 87
EP - 99
LA - eng
KW - Schatten-von Neumann classes; isotropic measure; Kahane-Khinchine inequalities; concentration inequalities
UR - http://eudml.org/doc/77926
ER -
References
top- [1] S. Alesker, -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. Zbl0834.52004
- [2] M. Anttila, K. Ball, I. Perissinaki, The central limit problem for convex bodies, Trans. Amer. Math. Soc.355 (12) (2003) 4723-4735. Zbl1033.52003MR1997580
- [3] K. Aomoto, Jacobi polynomials associated with Selberg integrals, SIAM J. Math. Anal.18 (2) (1987) 545-549. Zbl0639.33001MR876291
- [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. Zbl1039.52003MR2083388
- [6] C. Borell, Complements of Lyapunov's inequality, Math. Ann.205 (1973) 323-331. Zbl0248.26011MR323977
- [7] J. Bourgain, V.D. Milman, New volume ratio properties for convex symmetric bodies in , Invent. Math.88 (2) (1987) 319-340. Zbl0617.52006MR880954
- [8] A. Carbery, J. Wright, Distributional and norm inequalities for polynomials over convex bodies in , Math. Res. Lett.8 (2001) 233-248. Zbl0989.26010MR1839474
- [9] S. Chevet, 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. Zbl0395.60004
- [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. Zbl1067.46008MR1999610
- [11] H. König, M. Meyer, A. Pajor, The isotropy constants of the Schatten classes are bounded, Math. Ann.312 (1998) 773-783. Zbl0927.46014MR1660231
- [12] M.L. Mehta, Random Matrices, second ed., Academic Press, Boston, 1991. Zbl0780.60014MR1083764
- [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. Zbl0679.46012MR1008717
- [14] V.D. Milman, G. Schechtman, Asymptotic Theory of Finite-Dimensional Normed Spaces, Lecture Notes in Math., vol. 1200, Springer, Berlin, 1986. Zbl0606.46013MR856576
- [15] G. Paouris, Concentration of mass and central limit properties of isotropic convex bodies, Proc. Amer. Math. Soc.133 (2005) 565-575. Zbl1064.52005MR2093081
- [16] G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracks in Math., vol. 94, Cambridge Univ. Press, 1989. Zbl0698.46008MR1036275
- [17] J. Saint-Raymond, Le volume des idéaux d'opérateurs classiques, Studia Math.80 (1984) 63-75. Zbl0507.51015MR781729
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