Inégalités isopérimétriques en analyse et probabilités
Séminaire Bourbaki (1992-1993)
- Volume: 35, page 343-375
- ISSN: 0303-1179
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topLedoux, Michel. "Inégalités isopérimétriques en analyse et probabilités." Séminaire Bourbaki 35 (1992-1993): 343-375. <http://eudml.org/doc/110174>.
@article{Ledoux1992-1993,
author = {Ledoux, Michel},
journal = {Séminaire Bourbaki},
keywords = {isoperimetric inequalities; concentration measures},
language = {fre},
pages = {343-375},
publisher = {Société Mathématique de France},
title = {Inégalités isopérimétriques en analyse et probabilités},
url = {http://eudml.org/doc/110174},
volume = {35},
year = {1992-1993},
}
TY - JOUR
AU - Ledoux, Michel
TI - Inégalités isopérimétriques en analyse et probabilités
JO - Séminaire Bourbaki
PY - 1992-1993
PB - Société Mathématique de France
VL - 35
SP - 343
EP - 375
LA - fre
KW - isoperimetric inequalities; concentration measures
UR - http://eudml.org/doc/110174
ER -
References
top- [Az] K. Azuma. Weighted sums of certain dependent random variables. Tohoku Math. J.19, 357-367 (1967). Zbl0178.21103MR221571
- [Bae] A. Baernstein II. Integral means, univalent functions and circular symmetrization. Acta Math.133, 139-169 (1974). Zbl0315.30021MR417406
- [B-T] A. Baernstein II, B.A. Taylor. Spherical rearrangements, subharmonic functions and *-functions in n-space. Duke Math. J.43, 245-268 (1976). Zbl0331.31002MR402083
- [Ba] D. Bakry. L'hypercontractivité et son utilisation en théorie des semigroupes. École d'Été de Probabilités de St-Flour1992. Lecture Notes in Math.. Springer-Verlag. A paraître. Zbl0856.47026
- [B-É] D. Bakry, M. Émery. Diffusions hypercontractives. Séminaire de ProbabilitésXIX. Lecture Notes in Math.1123, 175-206 (1985). Springer-Verlag. Zbl0561.60080MR889476
- [Be] W. Beckner. Inequalities in Fourier analysis. Ann. Math.102,159-182 (1975). Zbl0338.42017MR385456
- [BA-L] G. BenArous, 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. Zbl0801.60019MR1354164
- [Ben] Y. Benyamini. Two point symmetrization, the isoperimetric inequality on the sphere and some applications. Texas Functional Analysis Seminar1983-84. The University of Texas (1984). MR832231
- [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). Zbl0571.53027MR788412
- [B-G-M] M. Berger, P. Gauduchon, E. Mazet. Le spectre d'une variété riemannienne. Lecture Notes in Math.194 (1971). Springer-Verlag. Zbl0223.53034MR282313
- [Bo1] C. Borell. The Brunn-Minskowski inequality in Gauss space. Invent. Math.30, 207-216 (1975). Zbl0292.60004MR399402
- [Bo2] C. Borell. Tail probabilities in Gauss space. Vector Space Measures and Applications, Dublin1977. Lecture Notes in Math.644, 71-82 (1978). Springer-Verlag. Zbl0397.60015MR502400
- [Bo3] C. Borell. On polynomials chaos and integrability. Prob. Math. Statist.3, 191-203 (1984). Zbl0555.60008MR764146
- [Bo4] C. Borell. Geometric bounds on the Ornstein-Uhlenbeck process. Z. Wahrscheinlichkeitstheor. verw. Gebiete70, 1-13 (1985). Zbl0537.60084MR795785
- [B-Z] Y.D. Burago, V.A. Zalgaller. Geometric inequalities. Springer-Verlag (1988). Première édition (en russe) : Nauka (1980). Zbl0633.53002MR936419
- [Bu] P. Buser. A note on the isoperimetric constant. Ann. scient. Éc. Norm. Sup.15, 213-230 (1982). Zbl0501.53030MR683635
- [C-F] I. Chavel, E. Feldman. Modified isoperimetric constants, and large time heat diffusion in Riemannian manifold. Duke Math. J.64, 473-499 (1991). Zbl0753.58031MR1141283
- [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). Zbl0611.58045MR630777
- [Ch] S. Chevet. Gaussian measures and large deviations. Probability in Banach spaces IV. Lecture Notes in Math.990, 30-46 (1983). Springer-Verlag. Zbl0527.60005MR707507
- [Co] T. Coulhon. Sobolev inequalities on graphs and on manifolds. Harmonic Analysis and Discrete Potential Theory, 207-214 (1991). Plenum Press. MR1222459
- [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.. Zbl0826.53035
- [C-SC] T. Coulhon, L. Saloff-Coste. Isopérimétrie pour les groupes et les variétés (1992). À paraître in Rev. Ibero Americana. Zbl0782.53066MR1232845
- [Da] E.B. Davies. Heat kernels and spectral theory. Cambridge Univ. Press (1989). Zbl0699.35006MR990239
- [Dv] A. Dvoretzky. Some results on convex bodies and Banach spaces. Proc. Symp. on Linear Spaces, Jerusalem, 123-160 (1961). Zbl0119.31803MR139079
- [D-F] P. Diaconis, D. Freedman. A dozen de Finetti-style results in search of a theory. Ann. Inst. H. Poincaré23, 397-423 (1987). Zbl0619.60039MR898502
- [Eh1] A. Ehrhard. Symétrisation dans l'espace de Gauss. Math. Scand.53, 281-301 (1983). Zbl0542.60003MR745081
- [Eh2] A. Ehrhard. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes. Ann. scient. Éc. Norm. Sup.17, 317-332 (1984). Zbl0546.49020MR760680
- [Eh3] A. Ehrhard. Eléments extrémaux pour les inégalités de Brunn-Minskowski gaussiennes. Ann. Inst. H. Poincaré22, 149-168 (1986). Zbl0595.60020MR850753
- [Eh4] A. Ehrhard. Sur l'inégalité de Sobolev logarithmique de Gross. Séminaire de ProbabilitésXVIII. Lecture Notes in Math.1059, 194-196 (1984). Springer-Verlag. Zbl0542.60040MR770961
- [Fa1] S. Fang. Isoperimetric inequalities on the Wiener space. Bull. Sc. Math.112, 345-355 (1988). Zbl0689.60026MR975368
- [Fa2] S. Fang. Grandes déviations pour le processus d'Ornstein-Uhlenbeck. Prépublication (1991).
- [Fe] H. Federer. Geometric measure theory. Springer-Verlag (1969). Zbl0874.49001
- [Fer1] X. Fernique. Intégrabilité des vecteurs gaussiens. C. R. Acad. Sci.Paris270, 1698-1699 (1970). Zbl0206.19002MR266263
- [Fer2] X. Fernique. Fonctions aléatoires gaussiennes, les résultats récents de M. Talagrand. Séminaire Bourbaki, exp. 660. Astérisque145-146, 177-186 (1987). Zbl0623.60052MR880032
- [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). Zbl0375.52002MR445274
- [G-H-L] S. Gallot, D. Hulin, J. Lafontaine. Riemannian Geometry. Deuxième édition, Springer-Verlag (1990). Zbl0636.53001MR1083149
- [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). Zbl0474.20018MR623534
- [G-M] M. Gromov, V.D. Milman. A topological application of the isoperimetric inequality. Amer. J. Math.105, 843-854 (1983). Zbl0522.53039MR708367
- [Gro] L. Gross. Logarithmic Sobolev inequalities. Amer. J. Math.97, 1061-1083 (1975). Zbl0318.46049MR420249
- [Gu] Y. Guivarc'h. Croissance polynômiale et périodes des fonctions harmoniques. Bull. Soc. Math. France101, 333-379 (1973). Zbl0294.43003MR369608
- [Ha] L.H. Harper. Optimal numbering and isoperimetric problems on graphs. J. Comb. Th.1, 385-393 (1966). Zbl0158.20802MR200192
- [Ka] J.-P. Kahane. Some random series of functions. Heath Math. Monographs (1968). Deuxième édition : Cambridge Univ. Press (1985). Zbl0192.53801MR833073
- [Ke] H. Kesten. On the speed of convergence in first-passage percolation (1991). À paraître in Ann. Appl. Probability. Zbl0783.60103MR1221154
- [K-L] J. Kuelbs, W. Li. Metric entropy and the small ball problem for Gaussian measures (1992). À paraître in J. Funct. Anal.. Zbl0799.46053MR1184915
- [L-S] H.J. Landau, L.A. Shepp. On the supremum of a Gaussian process. Sankhyà A32, 369-378 (1970). Zbl0218.60039MR286167
- [Led1] M. Ledoux. A note on large deviations for Wiener chaos. Séminaire de ProbabilitésXXIV. Lecture Notes in Math.1426, 1-14, Springer-Verlag (1990). Zbl0701.60020MR1071528
- [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). Zbl0752.53039MR1159831
- [Led3] M. Ledoux. Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space (1992). À paraître in Bull. Sc. math.. Zbl0841.49024MR1309086
- [Led4] M. Ledoux. A simple analytic proof of an inequality by P. Buser (1992). À paraître in Proc. Amer. Math. Soc.. Zbl0812.58093MR1186991
- [L-T1] M. Ledoux, M. Talagrand. Characterization of the law of the iterated logarithm in Banach spaces. Ann. Probability16, 1242-1264 (1988). Zbl0662.60008MR942766
- [L-T2] M. Ledoux, M. Talagrand. Probability in Banach spaces (Isoperimetry and processes). Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag (1991). Zbl0748.60004MR1102015
- [Lé] P. Lévy. Problèmes concrets d'analyse fonctionnelle. Gauthier-Villars (1951). Zbl0043.32302MR41346
- [L-Y] P. Li, S.-T. Yau. On the parabolic kernel of the Schrödinger operator. Acta Math.156, 153-201 (1986). Zbl0611.58045MR834612
- [MD] C.J.H. McDiarmid. On the method of bounded differences. Twelfth British Combinatorial Conference. Surveys in Combinatorics, 148-188 (1989). Cambrige Univ. Press. Zbl0712.05012MR1036755
- [MK] H.P. McKean. Geometry of differential space. Ann. Probability1, 197-206 (1973). Zbl0263.60035MR353471
- [Ma1] B. Maurey. Constructions de suites symétriques. C. R. Acad. Sci. Paris288, 679-681 (1979). Zbl0398.46019MR533901
- [Ma2] B. Maurey. Sous-espaces lp des espaces de Banach. Séminaire Bourbaki, exp. 608. Astérisque105-106, 199-216 (1983). Zbl0553.46020MR728989
- [Ma3] B. Maurey. Some deviations inequalities. Geometric and Funct. Anal.1, 188- 197 (1991). Zbl0756.60018MR1097258
- [Mi1] V.D. Milman. New proof of the theorem of Dvoretzky on sections of convex bodies. Funct. Anal. Appl.5, 28-37 (1971). Zbl0239.46018MR293374
- [Mi2] V.D. Milman. The heritage of P. Lévy in geometrical functional analysis. Colloque Paul Lévy sur les processus stochastiques. Astérisque157-158, 273- 302 (1988). Zbl0681.46021MR976223
- [Mi3] V.D. Milman. Dvoretzky's theorem - Thirty years later (Survey). Geometric and Funct. Anal.2, 455-479 (1992). Zbl0787.46016MR1191569
- [M-S] V.D. Milman, G. Schechtman. Asymptotic theory of finite dimensional normed spaces. Lecture Notes in Math.1200 (1986). Springer-Verlag. Zbl0606.46013MR856576
- [Mo] J. Moser. On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math.14, 557-591 (1961). Zbl0111.09302MR159138
- [N-S-W] A. Nagel, E. Stein, M. Wainger. Balls and metrics defined by vector fields. Acta Math.155, 103-147 (1985). Zbl0578.32044MR793239
- [Na] J. Nash. Continuity of solutions of parabolic and elliptic equations. Amer. J. Math.80, 931-954 (1958). Zbl0096.06902MR100158
- [Ne] E. Nelson. The free Markov field. J. Funct. Anal.12, 211-227 (1973). Zbl0273.60079MR343816
- [Os] R. Osserman. The isoperimetric inequality. Bull. Amer. Math. Soc.84, 1182- 1238 (1978). Zbl0411.52006MR500557
- [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. Zbl0606.60008MR864714
- [Pi2] G. Pisier. Riesz transforms : a simpler analytic proof of P. A. Meyer inequality. Séminaire de ProbabilitésXXII. Lecture Notes in Math.1321, 485-501, Springer-Verlag (1988). Zbl0645.60061MR960544
- [Pi3] G. Pisier. The volume of convex bodies and Banach space geometry. Cambridge Univ. Press (1989). Zbl0698.46008MR1036275
- [SC1] L. Saloff-Coste. Analyse sur les groupes de Lie à croissance polynômiale. Ark. för Math.28, 315-331 (1990). Zbl0715.43009MR1084020
- [SC2] L. Saloff-Coste. A note on Poincaré, Sobolev and Harnack inequalities. Duke Math. J.65, 27-38 (1992). Zbl0769.58054MR1150597
- [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). Zbl0030.07602MR28600
- [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). Zbl0395.28007MR365680
- [Ta1] M. Talagrand. Sur l'intégrabilité des vecteurs gaussiens. Z. Wahrscheinlichkeitstheor. verw. Gebiete68, 1-8 (1984). Zbl0529.60034MR767440
- [Ta2] M. Talagrand. Regularity of Gaussian processes. Acta Math.159, 99-149 (1987). Zbl0712.60044MR906527
- [Ta3] M. Talagrand. An isoperimetric theorem on the cube and the Khintchine-Kahane inequalities. Proc. Amer. Math. Soc.104, 905-909 (1988). Zbl0691.60015MR964871
- [Ta4] M. Talagrand. Small tails for the supremum of a Gaussian process. Ann. Inst. H. Poincaré24, 307-315 (1988). Zbl0641.60044MR953122
- [Ta5] M. Talagrand. Isoperimetry and integrability of the sum of independent Banach space valued random variables. Ann. Probability17, 1546-1570 (1989). Zbl0692.60016MR1048946
- [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 Seminar1989-90. Lecture Notes in Math.1469, 94-124 (1991). Springer-Verlag. Zbl0818.46047MR1122615
- [Ta8] M. Talagrand. Simple proof of the majorizing measure theorem. Geometric and Funct. Anal.2, 118-125 (1992). Zbl0760.60043MR1143666
- [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). Zbl0760.60005MR1097260
- [Ta10] M. Talagrand. On the rate of clustering in Strassen's law of the iterated logarithm. Probability in Banach spaces 8. Progress in Probability30, 339- 351 (1992). Birkhäuser. MR1227629
- [Ta11] M. Talagrand. Sharper bounds for Gaussian and empirical processes (1992). À paraître in Ann. Probability. Zbl0798.60051
- [Ta12] M. Talagrand. New Gaussian estimates for enlarged balls (1992). À paraître in Geometric and Funct. Anal.. Zbl0815.46021MR1233864
- [Ta13] M. Talagrand. Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem (1992). À paraître. Zbl0806.46035MR1215783
- [Ta14] M. Talagrand. Regularity of infinitely divisible processes. Ann. Probability21, 362-432 (1993). Zbl0776.60053MR1207231
- [Ta15] M. Talagrand. Concentration of measure and isoperimetric inequalities in product spaces. En préparation (1993). Zbl0864.60013
- [Va1] N. Varopoulos. Une généralisation du théorème de Hardy-Littlewood-Sobolev pour les espaces de Dirichlet. C. R. Acad. Sci. Paris299, 651-654 (1984). Zbl0566.31006MR770455
- [Va2] N. Varopoulos. Hardy-Littlewood theory for semigroups. J. Funct. Anal.63, 240-260 (1985). Zbl0608.47047MR803094
- [Va3] N. Varopoulos. Isoperimetric inequalities and Markov chains. J. Funct. Anal.63, 215-239 (1985). Zbl0573.60059MR803093
- [Va4] N. Varopoulos. Analysis on Lie groups. J. Funct. Anal.76, 346-410 (1988). Zbl0634.22008MR924464
- [Va5] N. Varopoulos. Small time Gaussian estimates of heat diffusion kernels. Part I : The semigroup technique. Bull. Sc. math.113, 253-277 (1989). Zbl0703.58052MR1016211
- [Va6] N. Varopoulos. Analysis and geometry on groups. Proceedings of the International Congress of Mathematicians, Kyoto (1990), vol. II, 951-957 (1991). Springer-Verlag. Zbl0744.43006MR1159280
- [V-SC-C] N. Varopoulos, L. Saloff-Coste, T. Coulhon. Analysis and geometry on groups. Cambridge Univ. Press (1992). Zbl0813.22003MR1218884
- [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). Zbl0362.05048MR438237
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