Inégalités isopérimétriques en analyse et probabilités

Ledoux, Michel

Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 773, 33 p.

MR Zbl

@incollection{SB_1992-1993__35__343_0,
     author = {Ledoux, Michel},
     title = {In\'egalit\'es isop\'erim\'etriques en analyse et probabilit\'es},
     booktitle = {S\'eminaire Bourbaki : volume 1992/93, expos\'es 760-774},
     series = {Ast\'erisque},
     note = {talk:773},
     pages = {343--375},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {216},
     year = {1993},
     mrnumber = {1246403},
     zbl = {0809.60021},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1992-1993__35__343_0/}
}

TY  - CHAP
AU  - Ledoux, Michel
TI  - Inégalités isopérimétriques en analyse et probabilités
BT  - Séminaire Bourbaki : volume 1992/93, exposés 760-774
AU  - Collectif
T3  - Astérisque
N1  - talk:773
PY  - 1993
SP  - 343
EP  - 375
IS  - 216
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1992-1993__35__343_0/
LA  - fr
ID  - SB_1992-1993__35__343_0
ER  -

%0 Book Section
%A Ledoux, Michel
%T Inégalités isopérimétriques en analyse et probabilités
%B Séminaire Bourbaki : volume 1992/93, exposés 760-774
%A Collectif
%S Astérisque
%Z talk:773
%D 1993
%P 343-375
%N 216
%I Société mathématique de France
%U http://archive.numdam.org/item/SB_1992-1993__35__343_0/
%G fr
%F SB_1992-1993__35__343_0

Ledoux, Michel. Inégalités isopérimétriques en analyse et probabilités, dans Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 773, 33 p. http://archive.numdam.org/item/SB_1992-1993__35__343_0/

Bibliographie
Cité par

[Az] K. Azuma. Weighted sums of certain dependent random variables. Tohoku Math. J. 19, 357-367 (1967). | MR | Zbl

[Bae] A. Baernstein Ii. Integral means, univalent functions and circular symmetrization. Acta Math. 133, 139-169 (1974). | MR | Zbl

[B-T] A. Baernstein Ii, B. A. Taylor. Spherical rearrangements, subharmonic functions and *-functions in n-space. Duke Math. J. 43, 245-268 (1976). | MR | Zbl

[Ba] D. Bakry. L'hypercontractivité et son utilisation en théorie des semigroupes. École d'Été de Probabilités de St-Flour 1992. Lecture Notes in Math.. Springer-Verlag. A paraître. | Zbl

[B-É] D. Bakry, M. Émery. Diffusions hypercontractives. Séminaire de Probabilités XIX. Lecture Notes in Math. 1123, 175-206 (1985). Springer-Verlag. | Numdam | MR | Zbl

[Be] W. Beckner. Inequalities in Fourier analysis. Ann. Math. 102,159-182 (1975). | MR | Zbl

[BA-L] G. Ben Arous, M. Ledoux. Schilder's large deviation principle without topology. Asymptotic problems in probability theory : Wiener functionals and asymptotics. Pitman Research Notes in Math. Series 284, 107-121 (1993). Longman. | MR | Zbl

[Ben] Y. Benyamini. Two point symmetrization, the isoperimetric inequality on the sphere and some applications. Texas Functional Analysis Seminar 1983-84. The University of Texas (1984). | MR

[B-B-G] P. Bérard, G. Besson, S. Gallot. Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov. Invent. Math. 80, 295-308 (1985). | MR | Zbl

[B-G-M] M. Berger, P. Gauduchon, E. Mazet. Le spectre d'une variété riemannienne. Lecture Notes in Math. 194 (1971). Springer-Verlag. | MR | Zbl

[Bo1] C. Borell. The Brunn-Minskowski inequality in Gauss space. Invent. Math. 30, 207-216 (1975). | MR | Zbl

[Bo2] C. Borell. Tail probabilities in Gauss space. Vector Space Measures and Applications, Dublin 1977. Lecture Notes in Math. 644, 71-82 (1978). Springer-Verlag. | MR | Zbl

[Bo3] C. Borell. On polynomials chaos and integrability. Prob. Math. Statist. 3, 191-203 (1984). | MR | Zbl

[Bo4] C. Borell. Geometric bounds on the Ornstein-Uhlenbeck process. Z. Wahrscheinlichkeitstheor. verw. Gebiete 70, 1-13 (1985). | MR | Zbl

[B-Z] Y. D. Burago, V. A. Zalgaller. Geometric inequalities. Springer-Verlag (1988). Première édition (en russe) : Nauka (1980). | MR | Zbl

[Bu] P. Buser. A note on the isoperimetric constant. Ann. scient. Éc. Norm. Sup. 15, 213-230 (1982). | Numdam | MR | Zbl

[C-F] I. Chavel, E. Feldman. Modified isoperimetric constants, and large time heat diffusion in Riemannian manifold. Duke Math. J. 64, 473-499 (1991). | MR | Zbl

[C-L-Y] S. Cheng, P. Li, S.-T. Yau. On the upper estimate of the heat kernel on a complete Riemannian manifold. Amer. J. Math. 156, 153-201 (1986). | MR | Zbl

[Ch] S. Chevet. Gaussian measures and large deviations. Probability in Banach spaces IV. Lecture Notes in Math. 990, 30-46 (1983). Springer-Verlag. | MR | Zbl

[Co] T. Coulhon. Sobolev inequalities on graphs and on manifolds. Harmonic Analysis and Discrete Potential Theory, 207-214 (1991). Plenum Press. | MR

[C-L] T. Coulhon, M. Ledoux. Isopérimétrie, décroissance du noyau de la chaleur et transformées de Riesz : un contre-exemple (1992). À paraître in Ark. för Math.. | Zbl

[C-SC] T. Coulhon, L. Saloff-Coste. Isopérimétrie pour les groupes et les variétés (1992). À paraître in Rev. Ibero Americana. | MR | Zbl

[Da] E. B. Davies. Heat kernels and spectral theory. Cambridge Univ. Press (1989). | MR | Zbl

[Dv] A. Dvoretzky. Some results on convex bodies and Banach spaces. Proc. Symp. on Linear Spaces, Jerusalem, 123-160 (1961). | MR | Zbl

[D-F] P. Diaconis, D. Freedman. A dozen de Finetti-style results in search of a theory. Ann. Inst. H. Poincaré 23, 397-423 (1987). | Numdam | MR | Zbl

[Eh1] A. Ehrhard. Symétrisation dans l'espace de Gauss. Math. Scand. 53, 281-301 (1983). | MR | Zbl

[Eh2] A. Ehrhard. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes. Ann. scient. Éc. Norm. Sup. 17, 317-332 (1984). | Numdam | MR | Zbl

[Eh3] A. Ehrhard. Eléments extrémaux pour les inégalités de Brunn-Minskowski gaussiennes. Ann. Inst. H. Poincaré 22, 149-168 (1986). | Numdam | MR | Zbl

[Eh4] A. Ehrhard. Sur l'inégalité de Sobolev logarithmique de Gross. Séminaire de Probabilités XVIII. Lecture Notes in Math. 1059, 194-196 (1984). Springer-Verlag. | Numdam | MR | Zbl

[Fa1] S. Fang. Isoperimetric inequalities on the Wiener space. Bull. Sc. Math. 112, 345-355 (1988). | MR | Zbl

[Fa2] S. Fang. Grandes déviations pour le processus d'Ornstein-Uhlenbeck. Prépublication (1991).

[Fe] H. Federer. Geometric measure theory. Springer-Verlag (1969). | Zbl

[Fer1] X. Fernique. Intégrabilité des vecteurs gaussiens. C. R. Acad. Sci. Paris 270, 1698-1699 (1970). | MR | Zbl

[Fer2] X. Fernique. Fonctions aléatoires gaussiennes, les résultats récents de M. Talagrand. Séminaire Bourbaki, exp. 660. Astérisque 145-146, 177-186 (1987). | Numdam | MR | Zbl

[F-L-M] T. Figiel, J. Lindenstrauss, V. D. Milman. The dimensions of almost spherical sections of convex bodies. Acta Math. 139, 52-94 (1977). | MR | Zbl

[G-H-L] S. Gallot, D. Hulin, J. Lafontaine. Riemannian Geometry. Deuxième édition, Springer-Verlag (1990). | MR | Zbl

[Gr1] M. Gromov. Paul Lévy's isoperimetric inequality. Prépublication I.H.E.S. (1980).

[Gr2] M. Gromov. Groups of polynomial growth and expanding maps. Publ. Math. I.H.E.S. 53, 53-78 (1981). | Numdam | MR | Zbl

[G-M] M. Gromov, V. D. Milman. A topological application of the isoperimetric inequality. Amer. J. Math. 105, 843-854 (1983). | MR | Zbl

[Gro] L. Gross. Logarithmic Sobolev inequalities. Amer. J. Math. 97, 1061-1083 (1975). | MR | Zbl

[Gu] Y. Guivarc'H. Croissance polynômiale et périodes des fonctions harmoniques. Bull. Soc. Math. France 101, 333-379 (1973). | Numdam | MR | Zbl

[Ha] L. H. Harper. Optimal numbering and isoperimetric problems on graphs. J. Comb. Th. 1, 385-393 (1966). | MR | Zbl

[Ka] J.-P. Kahane. Some random series of functions. Heath Math. Monographs (1968). Deuxième édition : Cambridge Univ. Press (1985). | MR | Zbl

[Ke] H. Kesten. On the speed of convergence in first-passage percolation (1991). À paraître in Ann. Appl. Probability. | MR | Zbl

[K-L] J. Kuelbs, W. Li. Metric entropy and the small ball problem for Gaussian measures (1992). À paraître in J. Funct. Anal.. | MR | Zbl

[L-S] H. J. Landau, L. A. Shepp. On the supremum of a Gaussian process. Sankhyà A32, 369-378 (1970). | MR | Zbl

[Led1] M. Ledoux. A note on large deviations for Wiener chaos. Séminaire de Probabilités XXIV. Lecture Notes in Math. 1426, 1-14, Springer-Verlag (1990). | Numdam | MR | Zbl

[Led2] M. Ledoux. A heat semigroup approach to concentration on the sphere and on a compact Riemannian manifold. Geometric and Funct. Anal. 2, 221-224 (1992). | MR | Zbl

[Led3] M. Ledoux. Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space (1992). À paraître in Bull. Sc. math.. | MR | Zbl

[Led4] M. Ledoux. A simple analytic proof of an inequality by P. Buser (1992). À paraître in Proc. Amer. Math. Soc.. | MR | Zbl

[L-T1] M. Ledoux, M. Talagrand. Characterization of the law of the iterated logarithm in Banach spaces. Ann. Probability 16, 1242-1264 (1988). | MR | Zbl

[L-T2] M. Ledoux, M. Talagrand. Probability in Banach spaces (Isoperimetry and processes). Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag (1991). | MR | Zbl

[Lé] P. Lévy. Problèmes concrets d'analyse fonctionnelle. Gauthier-Villars (1951). | MR | Zbl

[L-Y] P. Li, S.-T. Yau. On the parabolic kernel of the Schrödinger operator. Acta Math. 156, 153-201 (1986). | MR | Zbl

[MD] C. J. H. Mcdiarmid. On the method of bounded differences. Twelfth British Combinatorial Conference. Surveys in Combinatorics, 148-188 (1989). Cambrige Univ. Press. | MR | Zbl

[MK] H. P. Mckean. Geometry of differential space. Ann. Probability 1, 197-206 (1973). | MR | Zbl

[Ma1] B. Maurey. Constructions de suites symétriques. C. R. Acad. Sci. Paris 288, 679-681 (1979). | MR | Zbl

[Ma2] B. Maurey. Sous-espaces lp des espaces de Banach. Séminaire Bourbaki, exp. 608. Astérisque 105-106, 199-216 (1983). | Numdam | MR | Zbl

[Ma3] B. Maurey. Some deviations inequalities. Geometric and Funct. Anal. 1, 188- 197 (1991). | MR | Zbl

[Mi1] V. D. Milman. New proof of the theorem of Dvoretzky on sections of convex bodies. Funct. Anal. Appl. 5, 28-37 (1971). | MR | Zbl

[Mi2] V. D. Milman. The heritage of P. Lévy in geometrical functional analysis. Colloque Paul Lévy sur les processus stochastiques. Astérisque 157-158, 273- 302 (1988). | MR | Zbl

[Mi3] V. D. Milman. Dvoretzky's theorem - Thirty years later (Survey). Geometric and Funct. Anal. 2, 455-479 (1992). | MR | Zbl

[M-S] V. D. Milman, G. Schechtman. Asymptotic theory of finite dimensional normed spaces. Lecture Notes in Math. 1200 (1986). Springer-Verlag. | MR | Zbl

[Mo] J. Moser. On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 14, 557-591 (1961). | MR | Zbl

[N-S-W] A. Nagel, E. Stein, M. Wainger. Balls and metrics defined by vector fields. Acta Math. 155, 103-147 (1985). | MR | Zbl

[Na] J. Nash. Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80, 931-954 (1958). | MR | Zbl

[Ne] E. Nelson. The free Markov field. J. Funct. Anal. 12, 211-227 (1973). | MR | Zbl

[Os] R. Osserman. The isoperimetric inequality. Bull. Amer. Math. Soc. 84, 1182- 1238 (1978). | MR | Zbl

[Pi1] G. Pisier. Probabilistic methods in the geometry of Banach spaces. Probability and Analysis, Varenna (Italy) 1985. Lecture Notes in Math. 1206, 167-241 (1986). Springer-Verlag. | MR | Zbl

[Pi2] G. Pisier. Riesz transforms : a simpler analytic proof of P. A. Meyer inequality. Séminaire de Probabilités XXII. Lecture Notes in Math. 1321, 485-501, Springer-Verlag (1988). | Numdam | MR | Zbl

[Pi3] G. Pisier. The volume of convex bodies and Banach space geometry. Cambridge Univ. Press (1989). | MR | Zbl

[SC1] L. Saloff-Coste. Analyse sur les groupes de Lie à croissance polynômiale. Ark. för Math. 28, 315-331 (1990). | MR | Zbl

[SC2] L. Saloff-Coste. A note on Poincaré, Sobolev and Harnack inequalities. Duke Math. J. 65, 27-38 (1992). | MR | Zbl

[Sc] E. Schmidt. Die Brunn-Minkowskische Ungleichung und ihr Spiegelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie. Math. Nach. 1, 81-157 (1948). | MR | Zbl

[S-T] V. N. Sudakov, B. S. Tsirel'Son. Extremal properties of half-spaces for spherically invariant measures. J. Soviet. Math. 9, 9-18 (1978) ; translated from Zap. Nauch. Sem. L.O.M.I. 41, 14-24 (1974). | MR | Zbl

[Ta1] M. Talagrand. Sur l'intégrabilité des vecteurs gaussiens. Z. Wahrscheinlichkeitstheor. verw. Gebiete 68, 1-8 (1984). | MR | Zbl

[Ta2] M. Talagrand. Regularity of Gaussian processes. Acta Math. 159, 99-149 (1987). | MR | Zbl

[Ta3] M. Talagrand. An isoperimetric theorem on the cube and the Khintchine-Kahane inequalities. Proc. Amer. Math. Soc. 104, 905-909 (1988). | MR | Zbl

[Ta4] M. Talagrand. Small tails for the supremum of a Gaussian process. Ann. Inst. H. Poincaré 24, 307-315 (1988). | Numdam | MR | Zbl

[Ta5] M. Talagrand. Isoperimetry and integrability of the sum of independent Banach space valued random variables. Ann. Probability 17, 1546-1570 (1989). | MR | Zbl

[Ta6] M. Talagrand. Supremum of some canonical processes (1990). À paraître in J. Amer. Math. Soc..

[Ta7] M. Talagrand. A new isoperimetric inequality and the concentration of measure phenomenon. Geometric Aspects of Functional Analysis, Israel Seminar 1989-90. Lecture Notes in Math. 1469, 94-124 (1991). Springer-Verlag. | MR | Zbl

[Ta8] M. Talagrand. Simple proof of the majorizing measure theorem. Geometric and Funct. Anal. 2, 118-125 (1992). | MR | Zbl

[Ta9] M. Talagrand. A new isoperimetric inequality for product measure and the tails of sums of independent random variables. Geometric and Funct. Anal. 1, 211-223 (1991). | MR | Zbl

[Ta10] M. Talagrand. On the rate of clustering in Strassen's law of the iterated logarithm. Probability in Banach spaces 8. Progress in Probability 30, 339- 351 (1992). Birkhäuser. | MR

[Ta11] M. Talagrand. Sharper bounds for Gaussian and empirical processes (1992). À paraître in Ann. Probability. | Zbl

[Ta12] M. Talagrand. New Gaussian estimates for enlarged balls (1992). À paraître in Geometric and Funct. Anal.. | MR | Zbl

[Ta13] M. Talagrand. Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem (1992). À paraître. | MR | Zbl

[Ta14] M. Talagrand. Regularity of infinitely divisible processes. Ann. Probability 21, 362-432 (1993). | MR | Zbl

[Ta15] M. Talagrand. Concentration of measure and isoperimetric inequalities in product spaces. En préparation (1993). | Numdam | Zbl

[Va1] N. Varopoulos. Une généralisation du théorème de Hardy-Littlewood-Sobolev pour les espaces de Dirichlet. C. R. Acad. Sci. Paris 299, 651-654 (1984). | MR | Zbl

[Va2] N. Varopoulos. Hardy-Littlewood theory for semigroups. J. Funct. Anal. 63, 240-260 (1985). | MR | Zbl

[Va3] N. Varopoulos. Isoperimetric inequalities and Markov chains. J. Funct. Anal. 63, 215-239 (1985). | MR | Zbl

[Va4] N. Varopoulos. Analysis on Lie groups. J. Funct. Anal. 76, 346-410 (1988). | MR | Zbl

[Va5] N. Varopoulos. Small time Gaussian estimates of heat diffusion kernels. Part I : The semigroup technique. Bull. Sc. math. 113, 253-277 (1989). | MR | Zbl

[Va6] N. Varopoulos. Analysis and geometry on groups. Proceedings of the International Congress of Mathematicians, Kyoto (1990), vol. II, 951-957 (1991). Springer-Verlag. | MR | Zbl

[V-SC-C] N. Varopoulos, L. Saloff-Coste, T. Coulhon. Analysis and geometry on groups. Cambridge Univ. Press (1992). | MR

[W-W] D. L. Wang, P. Wang. Extremal configurations on a discrete torus and a generalization of the generalized Macaulay theorem. Siam J. Appl. Math. 33, 55-59 (1977). | MR | Zbl