@incollection{AST_2010__332__287_0, author = {Barthe, Frank}, title = {Un th\'eor\`eme de la limite centrale pour les ensembles convexes [d'apr\`es {Klartag} et {Fleury-Gu\'edon-Paouris]}}, booktitle = {S\'eminaire Bourbaki : volume 2008/2009 expos\'es 997-1011 - Avec table par noms d'auteurs de 1848/49 \`a 2008/09}, series = {Ast\'erisque}, note = {talk:1007}, pages = {287--304}, publisher = {Soci\'et\'e math\'ematique de France}, number = {332}, year = {2010}, mrnumber = {2648682}, zbl = {1217.46006}, language = {fr}, url = {http://archive.numdam.org/item/AST_2010__332__287_0/} }
TY - CHAP AU - Barthe, Frank TI - Un théorème de la limite centrale pour les ensembles convexes [d'après Klartag et Fleury-Guédon-Paouris] BT - Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09 AU - Collectif T3 - Astérisque N1 - talk:1007 PY - 2010 SP - 287 EP - 304 IS - 332 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2010__332__287_0/ LA - fr ID - AST_2010__332__287_0 ER -
%0 Book Section %A Barthe, Frank %T Un théorème de la limite centrale pour les ensembles convexes [d'après Klartag et Fleury-Guédon-Paouris] %B Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09 %A Collectif %S Astérisque %Z talk:1007 %D 2010 %P 287-304 %N 332 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2010__332__287_0/ %G fr %F AST_2010__332__287_0
Barthe, Frank. Un théorème de la limite centrale pour les ensembles convexes [d'après Klartag et Fleury-Guédon-Paouris], in Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Talk no. 1007, 18 p. http://archive.numdam.org/item/AST_2010__332__287_0/
[1] -estimate for the Euclidean norm on a convex body in isotropic position, in Geometric aspects of functional analysis (Israel, 1992-1994), Oper. Theory Adv. Appl., vol. 77, Birkhauser, 1995, p. 1-4. | MR | Zbl
-[2] The central limit problem for convex bodies, Trans. Amer. Math. Soc. 355 (2003), p. 4723-4735. | DOI | MR | Zbl
, & -[3] Remarks on non-interacting conservative spin systems : the case of gamma distributions, Stochastic Process. Appl. 119 (2009), p. 2711-2723. | DOI | MR | Zbl
& -[4] On concentration of distributions of random weighted sums, Ann. Probab. 31 (2003), p. 195-215. | DOI | MR | Zbl
-[5] On isoperimetric constants for log-concave probability distributions, in Geometric aspects of functional analysis, Lecture Notes in Math., vol. 1910, Springer, 2007, p. 81-88. | DOI | MR | Zbl
,[6] On the central limit property of convex bodies, in Geometric aspects of functional analysis, Lecture Notes in Math., vol. 1807, Springer, 2003, p. 44-52. | DOI | MR | Zbl
& -[7] Large deviations of typical linear functional on a convex body with unconditional basis, in Stochastic inequalities and applications, Progr. Probab., vol. 56, Birkhäuser, 2003, p. 3-13. | DOI | MR | Zbl
& -[8] On convex bodies and log-concave probability measures with unconditional basis, in Geometric aspects of functional analysis, Lecture Notes in Math., vol. 1807, Springer, 2003, p. 53-69. | DOI | MR | Zbl
& ,[9] Convex measures on locally convex spaces, Ark. Mat. 12 (1974), p. 239-252. | DOI | MR | Zbl
-[10] Moment inequalities and central limit properties of isotropic convex bodies, Math. Z. 240 (2002), p. 37-51. | DOI | MR | Zbl
, & , -[11] Permanence of moment estimates for -products of convex bodies, Studia Math. 150 (2002), p. 243-260. | DOI | EuDML | MR | Zbl
, & -[12] Asymptotics of cross sections for convex bodies, Beiträge Algebra Geom. 41 (2000), p. 437-454. | EuDML | MR | Zbl
& -[13] A dozen de Finetti-style results in search of a theory, Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), p. 397-423. | EuDML | Numdam | MR | Zbl
& -[14] Between Paouris concentration inequality and variance conjecture, à paraître dans Ann. Inst. H. Poincaré Probab. Statist, 2009. | EuDML | Numdam | MR | Zbl
-[15] Concentration in a thin Euclidean shell for log-concave measures, prépublication, 2009. | Zbl
,[16] A stability result for mean width of -centroid bodies, Adv. Math. 214 (2007), p. 865-877. | DOI | Zbl
, & -[17] A note on subgaussian estimates for linear functionals on convex bodies, Proc. Amer. Math. Soc. 135 (2007), p. 2599-2606. | DOI | Zbl
, & -[18] Extensions of Lipschitz mappings into a Hilbert space, in Conference in modern analysis and probability (New Haven, Conn., 1982), Contemp. Math., vol. 26, Amer. Math. Soc., 1984, p. 189-206. | DOI | Zbl
& -[19] Isoperimetric problems for convex bodies and a localization lemma, Discrete Comput. Geom. 13 (1995), p. 541-559. | DOI | EuDML | Zbl
, & -[20] On convex perturbations with a bounded isotropic constant, Geom. Fund. Anal. 16 (2006), p. 1274-1290. | DOI | Zbl
-[21] A central limit theorem for convex sets, Invent Math. 168 (2007), p. 91-131. | DOI | Zbl
,[22] Power-law estimates for the central limit theorem for convex sets, J. Fund. Anal. 245 (2007), p. 284-310. | DOI | Zbl
,[23] Uniform almost sub-Gaussian estimates for linear functionals on convex sets, Algebra i Analiz 19 (2007), p. 109-148. | Zbl
,[24] A Berry-Esseen type inequality for convex bodies with an unconditional basis, Probab. Theory Related Fields 45 (2009), p. 1-33. | DOI | Zbl
,[25] Average volume of sections of star bodies, in Geometric aspects of functional analysis, Lecture Notes in Math., vol. 1745, Springer, 2000, p. 119-146. | DOI | Zbl
& -[26] On the infimum convolution inequality, Studia Math. 189 (2008), p. 147-187. | DOI | EuDML | Zbl
& -[27] Blaschke-Santaló inequalities, J. Differential Geom. 47 (1997), p. 1-16. | DOI | Zbl
& -[28] The central limit problem for random vectors with symmetries, J. Theoret. Probab. 20 (2007), p. 697-720. | DOI | Zbl
& -[29] Gaussian marginals of convex bodies with symmetries, Beiträge Algebra Geom. 50 (2009), p. 101-118. | EuDML | Zbl
-[30] On Gaussian marginals of uniformly convex bodies, J. Theoret. Probab. 22 (2009), p. 256-278. | DOI | Zbl
-[31] On the role of convexity in isoperimetry, spectral gap and concentration, Invent. Math. 177 (2009), p. 1-43. | DOI | Zbl
,[32] A new proof of A. Dvoretzky's theorem on cross-sections of convex bodies, Funkcional. Anal, i Priložen. 5 (1971), p. 28-37. | Zbl
-[33] Dvoretzky's theorem-thirty years later, Geom. Funct. Anal. 2 (1992), p. 455-479. | DOI | EuDML | Zbl
,[34] Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed -dimensional space, in Geometric aspects of functional analysis (1987-88), Lecture Notes in Math., vol. 1376, Springer, 1989, p. 64-104. | DOI | Zbl
& -[35] Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Math., vol. 1200, Springer, 1986. | Zbl
& -[36] Projecting the surface measure of the sphere of , Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), p. 241-261. | DOI | EuDML | Numdam | Zbl
& -[37] Concentration of mass and central limit properties of isotropic convex bodies, Proc. Amer. Math. Soc. 133 (2005), p. 565-575. | DOI | Zbl
-[38] Concentration of mass on convex bodies, Geom. Funct. Anal. 16 (2006), p. 1021-1049. | DOI | Zbl
,[39] The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge Univ. Press, 1989. | Zbl
-[40] On the volume of the intersection of two balls, Proc. Amer. Math. Soc. 110 (1990), p. 217-224. | Zbl
& -[41] Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension, in Geometric aspects of functional analysis, Lecture Notes in Math., vol. 1910, Springer, 2007, p. 271-295. | DOI | Zbl
-[42]An isoperimetric inequality on the balls, Ann. Inst. H. Poincaré Probab. Stat. 44 (2008), p. 362-373. | DOI | EuDML | Numdam | Zbl
,[43] Typical distributions of linear functionals in finite-dimensional spaces of high dimension, Dokl. Akad. Nauk SSSR 243 (1978), p. 1402-1405. | Zbl
-[44] The square negative correlation property for generalized Orlicz balls, in Geometric aspects of functional analysis, Lecture Notes in Math., vol. 1910, Springer, 2007, p. 305-313. | DOI | Zbl
-